Surface area and volume — Paper 3 · IGCSE Mathematics (9-1) 0980

2 (a) B A O C In the diagram, A, B and C are points on the circle, centre O. (i) On the diagram, draw a chord. [1] (ii) Explain why angle ABC is 90°. … [1] (b) The length of the edge of a cube is 8 cm. Calculate the surface area of this cube. … cm2 [2] (c) A cuboid measures 5 cm by 4 cm by 2 cm. (i) Calculate the volume of this cuboid. Give the units of your answer. … … [3] (ii) On the 1 cm2 grid, draw an accurate net of this cuboid. One face has been drawn for you. [3]

10 marks

Mark scheme: 2(a)(i) Chord correctly drawn 1 2(a)(ii) Angle [in a] semicircle [is 90º] 1 2(b) 384 2 M1 for 8 × 8[× 6] 2(c)(i) 40 2 M1 for 5 × 4 × 2 cm3 1 2(c)(ii) Correct net 3 B2 for 4 more correct faces in correct position B1 for 2 or 3 more correct faces in correct position

This question in 0980/31 Oct/Nov 2019

6 (a) NOT TO 3 cm SCALE 2 cm 6 cm The diagram shows a cuboid. On the 1 cm2 grid, complete the net of the cuboid. One face has been drawn for you. [3] (b) A cube has a surface area of 384 cm2. Find the length of one of its sides. … cm [3] (c) 4 cm NOT TO SCALE 12 cm 7 cm The diagram shows a right-angled triangular prism. Work out the volume of the prism. … cm3 [3]

9 marks

Mark scheme: 6(a) Correct ruled net of cuboid 3 B2 for 3 or 4 further correct faces drawn in the correct places or B1 for 1 or 2 further correct faces drawn in the correct places 6(b) 8 3 M1 for 384 ÷ 6 M1dep for their 64 6(c) 168 3 M2 for (7 × 4 ÷ 2) × 12 oe or M1 for (7 × 4 ÷ 2) or their area × 12

This question in 0980/32 May/June 2020

6 NOT TO SCALE 3 cm 6 cm 4 cm The diagram shows a right-angled triangular prism. (a) On the 1 cm2 grid, complete the net of the prism. One face has been drawn for you. [3] (b) Work out the surface area of the prism. … cm2 [3] (c) Work out the volume of the prism. … cm3 [2]

8 marks

Mark scheme: 6(a) Correct net 3 B2 for 2 or 3 correct faces in the correct place or B1 for 1 correct face in the correct place 6(b) 84 3 M2 for 5 × 6 + 6 × 4 + 6 × 3 oe or better or 6 × (5 + 4 + 3) oe or better or 2( 12 × 3 × 4) oe or better or M1 for one correct area 6(c) 36 2 M1 for 12 × 3 × 4 × 6 oe

This question in 0980/31 Oct/Nov 2020

7 (a) The diagram shows the net of a cuboid on a 1 cm 2 grid. A N B M C L D K E J F I G H (i) The net is folded to form the cuboid. (a) Write down which two corners join to corner A. … [1] (b) Write down the edge which joins with KL. … [1] (ii) Find the total surface area of the cuboid. … cm2 [2] (iii) Find the volume of the cuboid. … cm3 [2] (b) The diagram shows a cylinder with length L cm. The radius of the cylinder is 3.2 cm and the volume is 775 cm 3. NOT TO SCALE L cm (i) Calculate the value of L. L = … [3] (ii) Calculate the volume of a solid sphere with radius 3 cm. 4 3 [The volume, V, of a sphere with radius r is V = rr .] 3 … cm3 [2] (iii) Four of these spheres are placed inside the cylinder. Calculate the percentage of the cylinder that is empty. … % [3]

14 marks

Mark scheme: 7(a)(i)(a) C and G 1 7(a)(i)(b) HI 1 7(a)(ii) 76 2 M1 for one relevant area calculation 7(a)(iii) 40 2 M1 for 5 × 2 × 4 oe 7(b)(i) 24.1 or 24.08 to 24.09… 3 775 M2 for oe π × 3.2 2 or M1 for [775 =] π × 3.22 × L or better 7(b)(ii) 113 or 113.09 to 113.11… 2 4 × π × 33 M1 for oe 3 7(b)(iii) 41.6 to 41.7 3 775 −×4 their (b)(ii) M2 for [× 100] oe 775 4 × their (b)(ii) or [100 –] × 100 oe 775 or M1 for 775 – 4 × their (b)(ii) oe 4 × their (b)(ii) or oe 775 If 0 scored, SC1 for answer 85.4 to 85.42

This question in 0980/31 Oct/Nov 2021

4 (a) The diagram shows the net of a cuboid. NOT TO SCALE 5 cm 7.8 cm A (i) Work out the area of the shaded rectangle, A. … cm2 [2] (ii) The volume of the cuboid is 468 cm 3. Complete the statement. The dimensions of the cuboid are … cm by … cm by … cm [2] (b) A cylinder has a radius of 8 cm and a height of 12 cm. Calculate, in terms of r, the volume of the cylinder. … cm3 [2] (c) NOT TO 7 cm SCALE 12 cm The diagram shows a circle with a diameter of 7 cm and a parallelogram with a base of 12 cm. The circle touches two of the sides of the parallelogram. Calculate the shaded area. … cm2 [3]

9 marks

Mark scheme: 4(a)(i) 39 2 M1 for 7.8  5 or B1 for 7.8 and 5 marked on two correct sides of rectangle A 4(a)(ii) 5 7.8 12 2 468 468 M1FT for oe or for 7.8  5 their(i) 4(b) 768π final answer 2 M1 for π  82  12 oe 4(c) 45.5 or 45.51 to 45.52 3 M2 for 12 7 π  3.52 oe or M1 for 12  7 oe or M1 for π  3.52 oe

This question in 0980/32 May/June 2022

5 (a) NOT TO SCALE This rectangle has an area of 12 cm2 and a perimeter of 16 cm. NOT TO SCALE This shape is made from six of these rectangles. Find the area and perimeter of this shape. Area = … cm2 Perimeter = … cm [4] (b) NOT TO SCALE 11.7 cm 8.4 cm 16 cm Find the area of this triangle. … cm2 [2] (c) A circle has a circumference of 28 cm. Work out the radius of the circle. … cm [2] (d) A cube has a volume of 125 m3. Work out the surface area of the cube. … m2 [3]

11 marks

Mark scheme: 5(a) [a =] 72 4 B1 for [a =] 72 [p =] 52 AND B3 for [p =] 52 or B1 for lengths of 6 and 2 M1 for use of 6l + 8w 5(b) 67.2 2 16  8.4 M1 for oe 2 If M0 scored, SC1 for 101 to 101.4 …. 5(c) 4.46 2 M1 for 28 ÷ 2π oe 5(d) 150 3 M2 for 6 × ( 3 125 )2 oe or M1 for 3 125 oe

This question in 0980/32 May/June 2023

4 (a) The diagram shows a cuboid. NOT TO 2 cm SCALE 3 cm 5 cm (i) On the 1cm2 grid, complete the net of the cuboid. One face has been drawn for you. [3] (ii) Calculate the surface area of the cuboid. … cm2 [2] (b) The diagram shows two solids: a cube and a right-angled triangular prism. NOT TO SCALE 4 cm 6 cm 9 cm x cm Both solids have the same volume. Calculate the value of x. x = … [4]

9 marks

Mark scheme: 4(a)(i) Fully correct net 3 B2 for 3 or 4 extra correct faces in the correct places or B1 for 1 or 2 extra correct faces in the correct places 4(a)(ii) 62 2 M1 for [2 ] (5  2 + 3  2 + 5  3) oe 4(b) 12 4 M3 for 18x = 216 oe or 216 ÷ 18 oe OR M1 for 63 or 6  6  6 or 216 1 M1 for  4  x  9 oe or 18x 2 M1 for their 18x = 216 oe or better

This question in 0980/31 Oct/Nov 2023

7 (a) NOT TO 10 cm SCALE 4 cm 7 cm Find the perimeter of the triangle. … cm [1] (b) The diagram shows a shape made from rectangles. 18.6 cm 4 cm NOT TO 7 cm 7 cm SCALE 13.5 cm Calculate the area of the shape. … cm2 [3] (c) The diagram shows a right-angled triangle ABC. B NOT TO 27.2 cm SCALE A C 24 cm Calculate the area of the triangle. … cm2 [5] (d) Calculate the volume of a sphere with diameter 5.25 cm. 4 [The volume, V, of a sphere with radius r is V = rr 3.] 3 … cm3 [2]

11 marks

Mark scheme: 7(a) 21 1 7(b) 118.1 cao 3 M2 for 18.6 × 4 + (13.5 – 4) × (18.6 –7 – 7) oe or 2 × 4 × 7 + 13.5 × (18.6 –7 –7) oe or 18.6 × 13.5 – 2 ×7 × (13.5 – 4) oe or 2×4×7+ (13.5–4)×(18.6–7–7)+ (18.6– 7–7)×4 oe or B1 for 9.5 or 4.6 seen 7(c) 153.6 cao 5 B3 for 12.8 or M2 for 27.22 – 242 oe or M1 for AB2 + 242 = 27.22 oe AND M1 for 0.5 × 24 × their AB oe 7(d) 75.8 or 75.76 to 75.78 2 4  5.25 3 M1 for   oe 3  2 

This question in 0980/31 Oct/Nov 2024

8 (a) The diagram shows the net of a solid. 10 cm x cm NOT TO SCALE x cm (i) Write down the mathematical name of the solid. … [1] (ii) Find the volume of the solid when x = 4 . … cm3 [2] (iii) Write down an expression, in terms of x, for the volume of the solid. … cm3 [1] (iv) Find the value of x when the volume of the solid is 360 cm3. x = … [2] (b) (i) Complete the table of values for y = 2 x 2 + x . x 0 1 2 3 4 5 y 0 3 10 [2] (ii) On the grid, draw the graph of y = 2 x 2 + x for 0 G x G 5 . y 60 50 40 30 20 10 0 0 1 2 3 4 5 x [3] (iii) Use your graph to solve the equation 2x 2 + x = 30 for 0 G x G 5 . x = … [1]

12 marks

Mark scheme: 8(a)(i) Cuboid 1 8(a)(ii) 160 2 M1 for 4 × 4 × 10 oe 8(a)(iii) 10x2 oe final answer 1 8(a)(iv) 6 nfww 2 M1 for 10x2 = 360 oe or better or their (a)(iii) = 360 oe or better or 360 ÷10 8(b)(i) 21, 36, 55 2 B1 for 2 correct 8(b)(ii) Correct smooth curve 3 B2FT for 5 or 6 points correctly plotted or B1FT for 3 or 4 points correctly plotted 8(b)(iii) 3.5 to 3.7 1 FT their value of x when y = 30

This question in 0980/31 Oct/Nov 2024

23 A sphere has radius 8 cm. A cone has radius 8 cm and height h. The sphere and the cone have the same volume. Work out the height, h, of the cone. h = … cm [4] Question 24 is printed on the next page.

4 marks

Mark scheme: 23 32 4 4 3  π  8 3 M3 for [h =] oe 1 2  π  8 3 4 3 1 2 or M2 for π 8 =  π  8  h oe 3 3 4 3 1 2 or M1 for  π  8 oe or  π  8  h oe 3 3

This question in 0980/32 May/June 2025

13 (a) The surface area of a solid cube is 121.5 cm 2 . Calculate the length of the side of the cube. … cm [3] (b) 10 cm NOT TO h SCALE 15 cm The area of the trapezium is 106.25 cm 2. (i) Calculate the height of the trapezium. … cm [2] (ii) Convert 106.25 cm 2 into m2. … m2 [1]

6 marks

Mark scheme: 13(a) 4.5 nfww 3 121.5 M2 for oe 6 121.5 or M1 for oe 6 13(b)(i) 8.5 2 1 M1 for (10 + 15)h = 106.25 oe or better 2 13(b)(ii) 0.010625 cao 1

This question in 0980/31 Oct/Nov 2025