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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
6 The diagram shows a solid triangular prism.
Diagram NOT accurately drawn
8 cm
10 cm
15 cm
6 cm
Work out the total surface area of the triangular prism.
.............................................................. cm^2
(Total for Question 6 is 3 marks)
- November 2024 2H # 6
18 The diagram shows cuboid ABCDEFGH.
4 cm
A
Diagram NOT accurately drawn
B
D C
E F
5 cm
H G
AB = 5 cm AH = 4 cm The size of the angle between CH and the plane ABCD is 35°
Calculate the volume of the cuboid. Give your answer correct to 3 significant figures.
....................................................... cm^3
(Total for Question 18 is 5 marks)
9 ) (^) November 2020 2H # 18
Diagram NOT accurately drawn
A
B
D
C
7 cm
E
10 cm 12 cm
h cm
10 ) (^) 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)
...................................................... cm^3
(Total for Question 9 is 6 marks)
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)
12 ) June 2022 1H # 22
......................................................
(Total for Question 17 is 5 marks)
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
14 ) (^) June 2022 2HR # 24
15 ) November 2021 2H #
22 The diagram shows a sphere of diameter x cm and a pyramid ABCDE with a horizontal rectangular base BCDE. A
E D
B
Diagram NOT accurately drawn
x cm C
O^2 x^ cm
5 x cm x cm
The vertex A of the pyramid is vertically above the centre O of the base so that AB = AC = AD = AE.
BC = x cm, CD = 2 x cm and AO = 5 x cm.
The volume of the sphere is 288 π cm^3
Calculate the total surface area of the pyramid. Give your answer correct to the nearest cm^2
....................................................... cm^2
(Total for Question 22 is 6 marks)
