Surface area and volume — Paper 2 · IGCSE Mathematics - International 0607

2 The volume of a cube is 27 cm3. Find the total surface area. … cm2 [2]

2 marks

Mark scheme: 2 54 2 B1 for [side = ] 3 or better

This question in 0607/22 Oct/Nov 2017

12 The volume of a sphere is r cm3. 3 Find the radius of the sphere. … cm [2]

2 marks

Mark scheme: 12 2 2 4 3 32 M1 for πr = π oe 3 3

This question in 0607/23 Oct/Nov 2017

18 The surface area of a sphere with radius r is equal to the curved surface area of a cone with radius r and height h. Show that h = r k , where k is a constant. [4]

4 marks

Mark scheme: 18 M2 M1 for l 2 = h 2 + r 2 or 4 πr 2 = πrl 4πr 2 = πr × h 2 + r 2 16r 2 = h 2 + r 2 leading to A1 Dep on M2 scored h = r 15 A1

This question in 0607/21 Oct/Nov 2018

10 The volume of a sphere is 36r cubic centimetres. Find the radius of the sphere. … cm [2]

2 marks

Mark scheme: 10 3 2 4 3 M1 for × π× r = 36 π oe 3

This question in 0607/23 Oct/Nov 2018

7 NOT TO SCALE 3 cm 7 cm The diagram shows a hemisphere joined to a cone. The hemisphere has a radius of 3 cm. The cone has a radius of 3 cm and a height of 7 cm. The total volume of the shape is kr cm3. Find the value of k. k = … [3] 4

3 marks

Mark scheme: 7 39 3 1 4 3 B1 for × × π× 3 2 3 1 2 B1 for × π× 3 × 7 3

This question in 0607/21 Oct/Nov 2019

5 Find the volume of a cone with radius 3 cm and perpendicular height 8 cm. Give your answer in terms of r. … cm3 [2]

2 marks

Mark scheme: 5 24π 2 1 2 M1 for × π × 3 × 8 3

This question in 0607/21 May/June 2020

6 A cone has base radius 5 cm and height cm . 4 A hemisphere has radius r cm. The volume of the hemisphere is equal to the volume of the cone. Find the value of r. r = … [3]

3 marks

Mark scheme: 6 1 3 125 3 2 oe M2 for r3 =  or better 2 12 2 1 4 3 1 2 5 or M1 for  r and  5  2 3 3 4

This question in 0607/23 Oct/Nov 2022

16 The volume of a hemisphere with radius r cm is r cm 3 . 3 Find the value of r. r = … cm [3] Question 17 is printed on the next page.

3 marks

Mark scheme: 16 [ r = ] 2 3 3 32 M2 for r = or better 4 1 4 3 16 or M1 for  π r =  π oe 2 3 3

This question in 0607/22 Feb/March 2023

11 The volume of a cone is 18r cm 3 . The height of the cone is the same as the diameter of its base. Find the radius of the base. … cm [3]

3 marks

Mark scheme: 11 3 3 3 18 3 M2 for r = 2 or 1 2 M1 for πr (2 r ) = 18π oe or better 3

This question in 0607/21 Oct/Nov 2023

16 NOT TO SCALE 4 cm 3 cm The diagram shows a solid half cylinder. The radius of the cross-section is 3 cm. The length of the solid is 4 cm. Find the total surface area of the solid. Give your answer in terms of r. … cm2 [4]

4 marks

Mark scheme: 16 21π + 24 4 M3 for  1 2   1   2   3  +  4  2 3  + ( 2 3 4 )  2   2  OR 1 2 M1 for  2   3 2 1 M1 for 4  2 3 2

This question in 0607/22 Feb/March 2025