Surface area and volume — Paper 1 · IGCSE Mathematics 0580

15 For Examiner's Use NOT TO 200 cm SCALE 350 cm 350 cm A large tank, in the shape of a cuboid, has a square base of side 350 cm and height 200 cm. The tank is filled with water. Find, in litres, the volume of water it holds when full. Answer litres [3]

3 marks

Mark scheme: 15 24500 3 M1 for 350 x 350 x 200 or 3.5 x 3.5 x 2 soi A1 for 24500000 or 24.5 seen B1 for his ‘volume’ correctly converted to litres.

This question in 0580/11 Oct/Nov 2004

14 For 30 mm Examiner's Use NOT TO 2 mm SCALE An old Greek coin is a cylinder with a diameter of 30 millimetres and a thickness of 2 millimetres. Calculate, in cubic millimetres, the volume of the coin. [The volume of a cylinder, radius r, height h, is πr2h.] Answer mm3 [2]

2 marks

Mark scheme: 14 rounds to 1410 isw 2 M1 for π × 15 2 × 2 (or π × 1.5 2 × 0.2 ) (isw only for incorrect 2 SC1 if π × 30 × 2 calculated correctly rounding eg 1413 = 141) (rounds to 5650 or 5660) (allow 3(.0)used) 1.41 cm 3 is 2 marks, 1.41 or 5.65 implies M1

This question in 0580/11 May/June 2005

5 NOT TO l m SCALE l m l m A cube of side l metres has a volume of 20 cubic metres. Calculate the value of l. Answer l = [2]

2 marks

Mark scheme: 5 2.71(4….) 2 M1 for attempt at cube root of 20

This question in 0580/11 May/June 2006

18 For Examiner's Use NOT TO 3 cm SCALE 2 cm 4 cm The solid shown is a cuboid with length 4 cm, width 2 cm and height 3 cm. (a) Draw an accurate net of the cuboid on the grid below. [2] (b) Using your net, calculate the total surface area of the cuboid. Answer(b) cm2 [2]

4 marks

Mark scheme: 18 (a) Net of the cuboid 2 M1 for a net with 6 correct size rectangles. A1 for a fully correct net. (b) 52 2ft M1 for 5 or 6 areas calculated and added or SC1 for answer of 26. ft only if 5 or 6 rectangles are shown in part (a). 8

This question in 0580/11 May/June 2006

3 Find the volume of a cube with sides of 2.3 cm. Answer cm3 [1]

1 marks

Mark scheme: 3 12.2 or 12.17 or 12.167 1

This question in 0580/11 Oct/Nov 2009

3 Find the volume of a cube with sides of 3.8 cm. Answer cm3 [1]

1 marks

Mark scheme: 3 54.9 or 54.87 or 54.872 1

This question in 0580/12 Oct/Nov 2009

12 For Examiner's Use NOT TO SCALE 4 cm 7 cm The diagram shows a triangular prism of length 7 cm. The cross-section is an equilateral triangle of side 4 cm. Complete an accurate net of the prism. One rectangular face has been drawn for you. [3]

3 marks

Mark scheme: 12 Correct net layout 1 2 rectangles and 2 equilateral triangles (one on each side) in correct position to make a net. 2 accurate, 7 cm by 4 cm, rectangles on 1 top and bottom. 2 accurate equilateral triangles at the 1 within 2 mm of central grid line sides (height 3.3 cm to 3.7 cm)

This question in 0580/12 Oct/Nov 2009

19 The diagram shows a door, AEBCD, from a model of a house. Examiner's Use ABCD is a rectangle and AEB is a semi-circle. AD = 14 cm and DC = 6 cm. E A B NOT TO SCALE 14 cm D 6 cm C (a) Calculate the area of the door. Answer(a) cm2 [3] (b) The door is 2 millimetres thick. Calculate, in cubic centimetres, the volume of the door. Answer(b) cm3 [2] Question 20 is printed on the next page.

5 marks

Mark scheme: 19 (a) 98.1 or 3 M1 for 14 × 6 (+……) 98.13 to 98.14 M1 ind for π × 32 ÷ 2 (b) 19.6 or 2ft M1 for their (a) × figs 2 19.62 to 19.63 Figs 196…. implies M1

This question in 0580/12 May/June 2010

14 Examiner's Use 1.75 cm NOT TO SCALE 2.3 cm 4 cm The cuboid above has length 4 cm, width 2.3 cm and height 1.75 cm. Calculate the volume of the cuboid (a) in cubic centimetres, Answer(a) cm3 [2] (b) in cubic millimetres. Answer(b) mm3 [1]

3 marks

Mark scheme: 14 (a) 16.1 2 M1 for 4 × 2.3 × 1.75, or better (b) 16100 1ft 1000 × their (a) IGCSE – May/June 2010 0580 13

This question in 0580/13 May/June 2010

18 For Examiner's Use NOT TO SCALE 44 cm 35 cm A cylindrical tank, with radius 35 cm, is filled with water to a depth of 44 cm. (a) Calculate the area of the base of the tank. Answer(a) cm2 [2] (b) Calculate the volume of water in the tank. Answer(b) cm3 [1] (c) Change your answer to part (b) into litres. Answer(c) litres [1]

4 marks

Mark scheme: 18 (a) 3846 to 3849 or 3850 2 M1 for π × 352 or SC1 correct volume answer (b) 169224 to 169356 1ft ft their (a) × 44 or 169400 or 169000 (c) 169.2 to 169.4 or 169 1ft ft their (b) ÷ 1000 IGCSE – October/November 2010 0580 11 4 5 4 14

This question in 0580/11 Oct/Nov 2010

1 For Examiner's Use Write down the name of the solid that can be made from the net shown in the diagram. Answer [1]

1 marks

Mark scheme: Qu. Answers Mark Part Marks 1 Pyramid 1

This question in 0580/13 Oct/Nov 2010

13 For 85 km Examiner's Use NOT TO SCALE 0.65 m A water pipeline in Australia is a cylinder with radius 0.65 metres and length 85 kilometres. Calculate the volume of water the pipeline contains when it is full. Give your answer in cubic metres. Answer m3 [3]

3 marks

Mark scheme: 13 113 000 or 3 B1 for 85 000 112 795 to 112 840 M1 for π × 0.65 2 × figs 85

This question in 0580/12 Oct/Nov 2012

13 Complete each statement with the correct mathematical term. For Examiner's Use (a) This solid is a … [1] (b) This polygon is a regular … [1] (c) A B C Angle ABC is an … angle [1] _____________________________________________________________________________________

3 marks

Mark scheme: 13 (a) cuboid 1 condone [rectangular] prism (b) pentagon 1 (c) obtuse 1

This question in 0580/11 May/June 2013

14 (a) The perimeter of a square is 28 mm. Work out the length of one side of the square. Answer(a) … mm [1] (b) Calculate the volume of a cylinder with radius 5.2 cm and height 15 cm. Answer(b) … cm3 [2] _____________________________________________________________________________________

3 marks

Mark scheme: 14 (a) 7 1 (b) 1270 or 1274 2 M1 for π × 5.22 × 15 or 1274.2 to 1274.4 4 2 M1 f 420  1 

This question in 0580/11 May/June 2013

20 For Examiner′s Use The diagram shows part of the net of a cuboid. It is drawn full size. (a) Complete the net of the cuboid. [2] (b) Work out the volume of the cuboid. Write down the units of your answer. Answer(b) … … [3] _____________________________________________________________________________________

5 marks

Mark scheme: 20 (a) Net completed 2 With one 2 by 5, one 3 by 5 and two 2 by 3 rectangles correctly positioned B1 for 2 correct rectangles correctly positioned (b) 30 2 M1 for 3 × 2 × 5 cm3 1 Independent mark

This question in 0580/12 Oct/Nov 2013

11 The diagram shows a cuboid. NOT TO SCALE 15 cm h 8 cm The volume of this cuboid is 720 cm3. The width is 8 cm and the length is 15 cm. Calculate h, the height of the cuboid. Answer h = … cm [2] __________________________________________________________________________________________

2 marks

Mark scheme: 11 6 2 M1 for 720 = 8 × 15 × h or better IGCSE – May/June 2014 0580 11

This question in 0580/11 May/June 2014

20 NOT TO SCALE 6.7 cm Each edge of this cube is 6.7 cm long. Work out (a) the volume, Answer(a) … cm3 [2] (b) the surface area. Answer(b) … cm2 [2] __________________________________________________________________________________________

4 marks

Mark scheme: 20 (a) 300.763 cao 2 M1 for 6.73 oe (b) 269.34 cao 2 M1 for 6.72 × 6 oe 2

This question in 0580/12 May/June 2014

9 A cylinder has radius 3.6 cm and height 16 cm. Calculate the volume of the cylinder. Answer … cm3 [2] __________________________________________________________________________________________

2 marks

Mark scheme: 9 651 to 652 2 M1 for π × 6.3 2 × 16 or better

This question in 0580/11 Oct/Nov 2014

15 A cuboid has volume 288 cm3. (a) The cuboid has length 12 cm and width 5 cm. Calculate the height of the cuboid. Answer(a) … cm [2] (b) 1 cm3 of the cuboid has a mass of 4 g. Work out the mass of the cuboid. Answer(b) … g [1] __________________________________________________________________________________________

3 marks

Mark scheme: 15 (a) 4.8 2 M1 for 288 ÷ (12 × 5) oe (b) 1152 1 9 63

This question in 0580/11 May/June 2015

20 (a) A cylinder has diameter 12 cm and length 18 cm. NOT TO SCALE 12 cm 18 cm Calculate the volume of the cylinder. Answer(a) … cm3 [2] (b) NOT TO SCALE 14 cm 8 cm 20 cm (i) Calculate the surface area of this cuboid. Answer(b)(i) … cm2 [3] (ii) Write your answer to part (b)(i) in square millimetres. Answer(b)(ii) … mm2 [1]

6 marks

Mark scheme: 20 (a) 2040 or 2036 or 2035.7 to 2036.1 2 M1 for π × 62 × 18 If zero, SC1 for answer of 8140 (after use of diameter) (b)(i) 1104 3 M2 for 2×(20×14 + 20×8 + 8×14) oe or M1 for 20×14 + 20×8 + 8×14 (b)(ii) their (b)(i) × 100 1FT

This question in 0580/13 May/June 2015

15 NOT TO SCALE 5 cm 9 cm 12.5 cm Calculate the volume of this cuboid. Give the units of your answer. Answer … … [3] __________________________________________________________________________________________

3 marks

Mark scheme: 15 562.5 2 M1 for 5 × 12.5 × 9 cm3 1 8 2 3

This question in 0580/13 Oct/Nov 2015

5 A cube has volume 1331 cm3. Calculate the length of one edge of the cube. … cm [1]

1 marks

Mark scheme: 5 11 1

This question in 0580/12 Feb/March 2016

22 (a) NOT TO 8 cm SCALE 7 cm 12 cm Calculate the volume of this cuboid. … cm3 [2] (b) Another cuboid has width 6 cm, height 9 cm and volume 675 cm3. Calculate the length of this cuboid. … cm [2] (c) The diagram shows a right-angled triangular prism. NOT TO SCALE 5 cm 24 cm 9 cm Calculate the volume of this prism. … cm3 [3]

7 marks

Mark scheme: 22 (a) 672 2 M1 for 12 × 8 × 7 (b) 12.5 2 M1 for 675 ÷ (6 × 9) (c) 540 3 M2 for (5 × 9 × 24) ÷ 2 oe or M1 for (5 × 9) ÷ 2 or 22.5 seen

This question in 0580/11 May/June 2016

22 7 cm NOT TO SCALE 6 cm 10 cm (a) Calculate the area of the trapezium. … cm2 [2] (b) The trapezium is the cross section of a prism. The length of the prism is 12 cm. Calculate the volume of the prism. Give the units of your answer. … … [2] Question 23 is printed on the next page.

4 marks

Mark scheme: 1 22 (a) 51 2 M1 for × (10 + 7) × 6 oe 2 (b) 612 1FT FT 12 × their (a) cm3 1

This question in 0580/12 May/June 2016

14 NOT TO 5 cm SCALE 6 cm 9 cm The diagram shows a solid in the shape of a cuboid with a small cube removed. The cuboid measures 9 cm by 6 cm by 5 cm. Each edge of the small cube measures 2 cm. Calculate the volume of the solid. … cm3 [3]

3 marks

Mark scheme: 14 262 3 M2 for 9 × 6 × 5 – 2 × 2 × 2 oe or M1 for 9 × 6 × 5 or 2 × 2 × 2 oe

This question in 0580/12 Oct/Nov 2016

22 A circle has a radius of 6.4 cm. (a) Work out the circumference of the circle. … cm [2] (b) The circle forms the top of a cylinder of height 12 cm. Work out the volume of the cylinder. … cm3 [2] Question 23 is printed on the next page.

4 marks

Mark scheme: 22 (a) 40.2 or 40.21 to 40.22 2 M1 for 2 × π × 6.4 oe (b) 1540 or 1544 2 M1 for π × 6.42 × 12 or 1544.1 to 1544.4

This question in 0580/13 Oct/Nov 2016

4 A cuboid has dimensions 12 m by 15 m by 20 m. Find the volume of the cuboid. … m3 [2]

2 marks

Mark scheme: 4 3600 2 M1 for 12 × 15 × 20

This question in 0580/12 Feb/March 2017

22 (a) Each diagram shows the net of a solid. Write down the mathematical name of each solid. (i) … [1] (ii) … [1] (b) The cross section of this prism is a trapezium. NOT TO SCALE 8 cm 5 cm 18 cm 14 cm Calculate the volume of the prism. … cm3 [3]

5 marks

Mark scheme: 22(a)(i) pyramid 1 22(a)(ii) triangular prism 1 22(b) 990 3 1 M2 for (8+14) × 5 × 18 oe 2 1 or M1 for (8+14) × 5 2

This question in 0580/12 May/June 2017

24 (a) Work out the area of a circle with radius 6 cm. … cm2 [2] (b) A solid cylinder has length 15 cm and radius 6 cm. NOT TO SCALE 6 cm 15 cm Calculate the total surface area of the cylinder. … cm2 [4]

6 marks

Mark scheme: 24(a) 113 or 113 to 113.12 2 M1 for π × 62 24(b) 792 or 791 or 791.4 to 791.8 4 M2 for 2 × π × 6 ×15 and M1FT for 2 × their (a) or 2 × π × 62

This question in 0580/12 May/June 2017

20 (a) NOT TO SCALE 6.7 cm 10.4 cm 9.2 cm 12.8 cm The diagram shows a small rectangle inside a large rectangle. Work out the shaded area. … cm2 [2] (b) NOT TO 5 cm SCALE 2 cm 8 cm Work out the surface area of this cuboid. … cm2 [3]

5 marks

Mark scheme: 20(a) 71.48 2 M1 for 12.8 × 10.4 or 9.2 × 6.7 or for an area of a suitable rectangle from shaded area 20(b) 132 3 M2 for 2 × (8 × 2 + 2 × 5 + 8 × 5) oe or M1 for at least two of 8 × 2, 8 × 5 and 2 × 5

This question in 0580/11 Oct/Nov 2017

21 The net of a solid is drawn on a 1 cm2 grid. (a) Write down the name of the solid made from this net. … [1] (b) Work out the volume of this solid. … cm3 [2]

3 marks

Mark scheme: 21(a) Cuboid 1 21(b) 24 2 M1 for 2 × 3 × 4

This question in 0580/11 May/June 2018

17 NOT TO SCALE 1 cm 7 cm The diagram shows a solid cuboid with base area 7 cm2. The volume of this cuboid is 21 cm3. Work out the total surface area. … cm2 [3]

3 marks

Mark scheme: 17 62 3 M1 for [height = ] 21 ÷ 7 M1 for 2(1 × their3 + their3 × 7 + 1 × 7) oe

This question in 0580/12 May/June 2018

20 A cylindrical glass has radius 3.6 cm and height 11 cm. It is filled with water. (a) Calculate, in cubic centimetres, the volume of water it contains. … cm3 [2] (b) Write your answer to part (a) in litres. … litres [1]

3 marks

Mark scheme: 20(a) 448 or 447.85 to 447.95 2 M1 for π × 3.62 × 11 20(b) [0].448 or [ 0].44785 to [0].44795 1 FT their (a) ÷ 1000

This question in 0580/12 May/June 2018

20 A water tank in the shape of a cuboid has length 1.5 metres and width 1 metre. The water in the tank is 60 centimetres deep. Calculate the number of litres of water in the tank. … litres [3]

3 marks

Mark scheme: 20 900 3 150 × 100 × 60 M2 for oe 1000 or M1 for 150 × 100 × 60 or 1.5 [× 1] × 0.6 or B1 for figs 9

This question in 0580/11 Oct/Nov 2018

7 The diagram shows a net of a solid. Write down the mathematical name of the solid. … [1]

1 marks

Mark scheme: 7 triangular prism 1

This question in 0580/12 Feb/March 2019

21 7.5 cm NOT TO SCALE 5 cm 12 cm Calculate the total surface area of the cuboid. … cm2 [3]

3 marks

Mark scheme: 21 375 3 M2 for 2 (12 × 5 + 12 × 7.5 + 5 × 7.5 ) oe or M1 for 12 × 5 or 12 × 7.5 or 5 × 7.5

This question in 0580/12 Feb/March 2019

6 The volume of a cuboid is 180 cm3. The base is a square of side length 6 cm. Calculate the height of this cuboid. … cm [2]

2 marks

Mark scheme: 6 5 2 M1 for 180 ÷ 62 oe

This question in 0580/11 May/June 2019

14 (a) The diagram shows a solid cuboid made of identical cubes. NOT TO SCALE Work out the number of cubes in the cuboid. … [1] (b) The diagram shows the nets of two solids. Write down, under each net, the mathematical name for the solid. … … [2]

3 marks

Mark scheme: 14(a) 160 1 14(b) Cone, [square based] pyramid 2 B1 for each

This question in 0580/12 May/June 2019

22 A closed box in the shape of a cuboid has length 5 cm, width 4 cm and height 2 cm. (a) Calculate the volume of the box. … cm3 [2] (b) On the 1 cm2 grid, complete the net of this box. [2]

4 marks

Mark scheme: 22(a) 40 2 M1 for 5 × 4 × 2 22(b) 4 correct rectangles only, added in 2 B1 for 2 correct rectangles in correct correct positions positions

This question in 0580/13 May/June 2019

11 A cone has radius 4.5 cm and height 10.4 cm. Calculate, in terms of r, the volume of the cone. 1 2 [The volume, V, of a cone with radius r and height h is V = rr h .] 3 … cm3 [2]

2 marks

Mark scheme: 11 70.2π 2 1 M1 for [π] × 4.52 × 10.4 3

This question in 0580/11 May/June 2020

11 NOT TO SCALE 10 cm A 12 cm h B 5 cm 8 cm 16 cm The diagram shows cuboid A and cuboid B. Cuboid A has the same volume as cuboid B. Calculate the height, h, of cuboid B. h = … cm [3]

3 marks

Mark scheme: 11 3 3 M2 for 12 × 8 × 5 ÷ (16 × 10) oe or M1 for 12 × 8 × 5 or 10 × 16 × h

This question in 0580/12 Oct/Nov 2020

12 (a) A cuboid has length 5 cm, width 4 cm and height 3 cm. On the 1 cm2 grid, complete the net of the cuboid. One face has been drawn for you. [3] (b) Find the volume of the cuboid. … cm3 [2]

5 marks

Mark scheme: 12(a) Complete correct ruled net 3 B2 for 3 or 4 correct rectangles in correct places or B1 for 1 or 2 correct rectangles in correct places 12(b) 60 2 M1 for 5 × 4 × 3

This question in 0580/13 Oct/Nov 2020

5 The volume of a cuboid is 24 cm3. The base of the cuboid is 3 cm by 2 cm. Draw a net of the cuboid on the 1cm2 grid. [4]

4 marks

Mark scheme: 5 Correct net of 6 faces drawn 4 B1 for height of 4 cm soi 24 or M1 for 3 × 2 B1 for a 3 cm by 2 cm face soi B1 for 3 more faces drawn in correct positions or for a complete net drawn with wrong height

This question in 0580/11 May/June 2021

16 A cuboid has a square base. The volume of this cuboid is 867 cm3 and its height is 12 cm. Calculate the length of one side of the square base. … cm [3]

3 marks

Mark scheme: 16 8.5 3 M2 for 867 ÷ 12 or M1 for 867 ÷ 12

This question in 0580/12 May/June 2021

18 (a) Calculate the volume of a cylindrical vase with radius 14.2 cm and height 18 cm. … cm3 [2] (b) Change your answer to part (a) into litres. … litres [1]

3 marks

Mark scheme: 18(a) 11 400 or 11 400 to 11 404 2 M1 for π × 14.22 × 18 oe 18(b) 11.4 or 11.4 to 11.40… 1 FT their (a) ÷ 1000

This question in 0580/13 May/June 2021

4 Write down the mathematical name of this solid. … [1]

1 marks

Mark scheme: 4 Cone 1

This question in 0580/13 Oct/Nov 2021

8 A box, in the shape of a cuboid, has volume 357 cm3. It has a length of 8.5 cm and a width of 6 cm. Calculate the height of the box. … cm [2]

2 marks

Mark scheme: 8 7 2 M1 for 357 ÷ (8.5 × 6)

This question in 0580/13 May/June 2022

18 NOT TO SCALE 6 cm 18 cm w cm The right-angled triangular prism has height 6 cm, width w cm and length 18 cm. The volume of the prism is 810 cm 3. Find the value of w. w = … [3]

3 marks

Mark scheme: 18 15 3 810 M2 for 1 2 6 18 1 or M1 for 6 w  18 [=810] 2 or 810 ÷ 18 or 810 ÷ 6 or 810 ÷ (6 × 18)

This question in 0580/12 Oct/Nov 2022

10 The diagram shows one face of a cuboid on a 1 cm 2 grid. The cuboid has a volume of 24 cm 3. Complete a net of this cuboid. [3]

3 marks

Mark scheme: 10 Fully correct net 3 B2 for 3 or 4 correct rectangles drawn in correct position or B1 for one correct face drawn in correct position or M1 for 24 ÷ (4 × 3) If 0 scored, SC1 for a net that makes a cuboid but the volume is not 24

This question in 0580/12 Feb/March 2023

26 A circle has an area of 25rcm 2. (a) Work out the circumference of the circle. Give your answer in terms of r. … cm [3] (b) Two of the circles are used as the ends of a cylinder, with height h cm. The total surface area of the cylinder is 170rcm 2. Work out the value of h. h = … [3]

6 marks

Mark scheme: 26(a) 10π 3 M1 for 25 π = πr 2 or B1 for r = 5 M1dep for 2π  theirr 26(b) 12 3 M2 for 25π +2 their10π =h 170π or better or M1 for 2  πr 2 + 2πrh = 170π or M1 for 170π −2 25π or better

This question in 0580/12 Feb/March 2023

13 Calculate the volume of a sphere with diameter 4.8 cm. 4 3 [The volume, V, of a sphere with radius r is V = rr .] 3 … cm3 [2]

2 marks

Mark scheme: 13 57.9 or 57.90 to 57.91…. 2 3 4  4.8  M1 for  π   3  2 

This question in 0580/11 May/June 2023

8 The surface area of a cube is 73.5 cm2. Find the length of one side of the cube. … cm [2]

2 marks

Mark scheme: 8 3.5 2 73.5 M1 for or better 6

This question in 0580/13 Oct/Nov 2023

12 10 cm NOT TO SCALE 4 cm 5 cm The diagram shows the net of a cuboid. (a) Work out the surface area of this cuboid. … cm2 [2] (b) Work out the volume of this cuboid. … cm3 [2]

4 marks

Mark scheme: 12(a) 220 2 M1 for [2]( 5  4 + 4  10 + 5  10 ) 12(b) 200 2 M1 for 5 4 10

This question in 0580/12 Feb/March 2024

10 h cm NOT TO SCALE 6 cm 15 cm The total surface area of this cuboid is 369 cm2. Work out the value of h. h = … [4]

4 marks

Mark scheme: 10 4.5 4 M3 for 2  6 h  15 h   369  2  6  15  or better or M2 for 2 6  15  6  h  15  h  oe or M1 for [2] 6  15 or [2] 6h or [2] 15h

This question in 0580/11 May/June 2024

16 A circle has an area of 36r cm 2 . (a) Find the circumference of the circle. Give your answer in terms of r. … cm [3] (b) The circle forms the base of a cylinder with height h cm. The volume of the cylinder is 540r cm 3 . Work out the value of h. h = … [2]

5 marks

Mark scheme: 16(a) 12π cao 3 B2 for r = 6 or M1 for πr2 = 36π oe 16(b) 15 cao 2 M1 for [h =] 540π ÷ 36π or better

This question in 0580/12 May/June 2024

23 0.5 m NOT TO 32 cm SCALE 24 cm The diagram shows a spherical tank with radius 0.5 m and a cylindrical jug with diameter 24 cm and height 32 cm. The tank is full of water. Calculate how many times the jug can be completely filled with water from the tank. 4 3 [The volume, V, of a sphere with radius r is rr .] 3 … [5]

5 marks

Mark scheme: 23 36 5 B4 for 36.16 to 36.17 or 36.2 or B1 for 50 or 0.12 and 0.32 M1 for 43 ×π×(their50)3 or 43 ×π× 0.53 M1 for π ×122×32 or π × their 0.122× their 0.32 M1 for their 523 598 ÷ their 14 476 or their 0.523 598 ÷ their 0.014 476 dep on M1 M1and correct formulae used If 1,2or 3 scored award SC1 for their decimal answer correctly rounded down to the nearest integer

This question in 0580/13 May/June 2024

14 C NOT TO SCALE 4 cm D 6 cm A 6 cm B The diagram shows a triangular prism. ABC is an isosceles triangle with AC = BC. The perpendicular height of triangle ABC is 4 cm. AB = 6 cm and BD = 6 cm. (a) Complete this statement. The prism has … faces and … edges. [2] (b) Show that the length of BC is 5 cm. [2] (c) Complete the net of the prism on the 1 cm 2grid. The base has been drawn for you. [3]

7 marks

Mark scheme: 14(a) 5 9 2 B1 for each 14(b) 2 2 2 2 2 3 + 4 [=5] M1 for 3 + 4 14(c) correct net drawn 3 B2 for 3 correct extra faces drawn in correct places or B1 for 1 correct extra face drawn in correct place

This question in 0580/12 Feb/March 2025

10 A cuboid has length 5 cm, width 2 cm and height 3 cm. (a) Draw a net of the cuboid on the 1 cm2 grid. [3] (b) Work out the volume of the cuboid. Give the units of your answer. … … [2]

5 marks

Mark scheme: 10(a) Fully correct net 3 B2 for 4 correct faces in correct places or B1 for 2 correct faces in correct places 10(b) 30 cm3 2 B1 for 30 B1 for cm3

This question in 0580/12 May/June 2025

8 The diagram shows two faces of a net of a cuboid on a 1 cm 2 grid. (a) Complete the statement. The dimensions of the cuboid are … cm by … cm by … cm. [1] (b) On the grid, complete a net of the cuboid. [3] (c) Work out the volume of the cuboid. … cm3 [2]

6 marks

Mark scheme: 8(a) 3, 3, 5 1 8(b) Fully correct net 3 B2 for 2 correct extra faces in correct places or B1 for 1 correct extra face in correct place 8(c) 45 2 FT their dimensions from (a) M1 for 3 × 3 × 5 oe

This question in 0580/13 May/June 2025