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- January 2022 1HR # 10
10 Jonty has a storage container in the shape of a cuboid, as shown in the diagram.
3 m
2.5 m
12 m
Diagram NOT accurately drawn
Jonty is going to paint the outside of his storage container, apart from the base which is shown shaded in the diagram. He needs enough paint to cover the four sides and the top.
Each tin of paint covers an area of 15 m^2
The cost of each tin of paint recently increased by 10% After the increase, the cost of each tin of paint is £26.
Jonty says
“ Before the increase, I could have bought enough paint for less than £200”
Show that Jonty is correct. Show your working clearly.
(Total for Question 10 is 6 marks)
5 The diagram shows a cylinder.
Diagram NOT accurately drawn
The radius of the cylinder is 70 cm The height of the cylinder is 18 cm
Work out the volume of the cylinder. Give your answer in litres correct to the nearest litre.
............................................................... litres
(Total for Question 5 is 4 marks)
- November 2024 1H # 5
4 ) November 2020 2H # 9
9 The diagram shows a solid cylinder with radius 3 m.
3 m (^) Diagram NOT accurately drawn
The volume of the cylinder is 72 ʌ m^3
Calculate the total surface area of the cylinder. Give your answer correct to 3 significant figures.
....................................................... m^2
(Total for Question 9 is 5 marks)
2 The diagram shows a solid triangular prism.
Diagram NOT accurately drawn
6 cm
7 cm 3.6 cm
4.8 cm
Work out the total surface area of the triangular prism. Give your answer correct to 3 significant figures.
...................................................... cm^2
(Total for Question 2 is 3 marks)
6 ) January 2023 1HR
7 ) January 2021 1H # 3
3 The diagram shows a container for water in the shape of a prism.
Diagram NOT accurately drawn
125 cm
40 cm
30 cm
60 cm
85 cm
20 cm
The rectangular base of the prism, shown shaded in the diagram, is horizontal. The container is completely full of water.
Tuah is going to use a pump to empty the water from the container so that the volume of water in the container decreases at a constant rate.
The pump starts to empty water from the container at 10 30 and at 12 00 the water level in the container has dropped by 20 cm.
Find the time at which all the water has been pumped out of the container.
......................................................
(Total for Question 3 is 4 marks)
Diagram NOT accurately drawn
A
B
D
C
7 cm
E
10 cm 12 cm
h cm
9 )Janaury 2020 2HR # 13
G F
H
The diagram shows a prism ABCDEFGH in which ABCD is a trapezium with BC parallel to AD and CDEF is a rectangle.
BC = 7 cm AD = 12 cm DE = 10 cm
The height of trapezium ABCD is h cm The volume of the prism is 608 cm 3
Work out the value of h.
h = .......................................................
(Total for Question 13 is 3 marks)
9 The diagram shows a rectangular sheet of metal ABCD
A
D
B
C
50 cm
Diagram NOT accurately drawn
BD = 50 cm and angle BDC = 32°
Nasser joins side AD to side BC to form a cylinder.
BC is the height of the cylinder. DC is the circumference of the cross section of the cylinder.
Work out the volume, in cm 3 , of the cylinder. Give your answer correct to 3 significant figures.
10 ) June 2023 2HR
22 A solid is made from a cone and a hemisphere.
20 cm Diagram NOT accurately drawn
The circular plane face of the hemisphere coincides with the circular base of the cone. The radius of the hemisphere and the radius of the circular base of the cone are both 20 cm.
The curved surface area of the cone is 580 π cm 2
The volume of the solid is kπ cm^3
Work out the exact value of k
k = ......................................................
(Total for Question 22 is 5 marks)
11 ) June 2022 1H # 22
17 A solid, S , is made from a hemisphere and a cylinder.
The centre of the circular face of the hemisphere and the centre of the top face of the cylinder are at the same point.
x cm
(20 – 4 x ) cm
Diagram NOT accurately drawn
The radius of the cylinder and the radius of the hemisphere are both x cm. The height of the cylinder is (20 – 4 x ) cm.
The volume of S is V cm 3 where V =
πy
Find the maximum value of y. Show clear algebraic working.
12 )January 2021 1H # 17
24 The diagram shows a frustum of a cone, and a sphere.
The frustum, shown shaded in the diagram, is made by removing the small cone from the large cone. The small cone and the large cone are similar. Diagram NOT accurately drawn
Small cone h cm
r cm r cm
Large cone kh cm
kr cm
The height of the small cone is h cm and the radius of the base of the small cone is r cm. The height of the large cone is kh cm and the radius of the base of the large cone is kr cm. The radius of the sphere is r cm.
The sphere is divided into two hemispheres, each of radius r cm.
Solid A is formed by joining one of the hemispheres to the frustum. The plane face of the hemisphere coincides with the upper plane face of the frustum, as shown in the diagram below.
Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone. The plane face of the hemisphere coincides with the plane face of the base of the small cone, as shown in the diagram below.
Diagram NOT accurately drawn A B
kr cm
r cm
13 ) (^) June 2022 2HR # 24
The volume of solid A is 6 times the volume of solid B.
Given that k > 37
find an expression for h in terms of k and r
h = .......................................................
(Total for Question 24 is 6 marks)
....................................................... cm^2
(Total for Question 22 is 6 marks)
20 The diagram shows a frustum of a cone and a sphere.
The frustum is made by removing a small cone from a large cone. The cones are similar.
h cm
2 h cm
r cm
r cm
Diagram NOT accurately drawn
The height of the small cone is h cm. The height of the large cone is 2 h cm. The radius of the base of the large cone is r cm.
The radius of the sphere is r cm.
Given that the volume of the frustum is equal to the volume of the sphere,
find an expression for r in terms of h. Give your expression in its simplest form.
15 ) January 2020 1HR # 20
