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Beaconhouse School System
Boys Campus, Canal Side
Crash Revision (Mensuration) XIC
1. The diagram shows solid A which is made from a hemisphere joined to a cone of equal radius.
The hemisphere and the cone each have radius 6 cm.
The total height of the solid is 18 cm.
(a) Show that the slant height, x cm,
of the cone is 13.4 cm, correct to 1 decimal place.
(b) Calculate the total surface area of solid A.
(c) Calculate the volume of solid A.
Answrs a) 13.42, b) 479 , c) 905
2. A cone has height 9.5 cm and volume 115 cm3.
(i) Show that the radius of the base of the cone is 3.4 cm,
correct to 1 decimal place
(ii) Calculate the curved surface area of the cone
Answers i) 3.40, ii) 107.8
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3. The diagram shows lamp A. It is made in the shape of a cylinder with a hemisphere on top.
The radius of the hemisphere and the radius of the cylinder are both 3 cm.
The total height of the lamp is 24 cm.
(i) Show that the volume of lamp A is 650 cm3, correct to 3 significant figures.
(ii) Calculate the curved surface area of lamp A.
Answers i) 650.4, ii) 21.23
4. The diagram shows a pyramid with a rectangular, horizontal base. Vertex F of the pyramid is
vertically above the centre of the base, E. AB = 6.2 cm and BC = 4.3 cm.
The length of each sloping edge of the pyramid is 9.5 cm.
(a) Show that the height, EF, of the pyramid is 8.72 cm,
correct to 3 significant figures.
(b) Calculate the volume of the pyramid
Answers a) 8.719, b) 77.50
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5. The diagram shows a bowl with a circular base.
The curved surface of the bowl is formed by removing a cone with radius 12 cm and height 45 cm
from a larger cone as shown in the diagram.
The radius of the top of the bowl is 16 cm and its height is 15 cm.
(a) Calculate the volume of the bowl.
(b) The slant height of the cone that has been removed is c cm.
Show that c = 46.6, correct to 3 significant figures.
(c) The bowl is completely filled with water.
Calculate the total surface area of the bowl that is in contact with the water.
Answers a) 9301, b) 46.57 , c) 1819
6. A birthday cake is in the shape of a cylinder.
There are two layers of cake and one layer of icing.
Each layer of cake has radius 10 cm and height 3 cm.
The icing, between the two layers of cake, has radius 10 cm and height 12 mm.
(a) Calculate the volume of icing in the birthday cake.
Give your answer in cm3.
(b) The top and curved surface of the birthday cake are now covered with chocolate.
Calculate the area of the birthday cake that is covered with chocolate .
Answers a) 377.04, b) 766.6
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7. The diagram shows a solid formed by joining a cylinder to a hemisphere.
The diameter of the cylinder is 9 cm and its height is 16 cm.
(i) The volume of the hemisphere is equal to the volume of the cylinder.
Show that the radius of the hemisphere is 7.86 cm, correct to 2 decimal places
(ii) Calculate the total surface area of the solid.
Answers i) 7.862., ii) 1030 or 1040
8. A cone has radius 6 cm and slant height l cm.
The total surface area of the cone is 84r cm2.
(a) Show that l = 8.
(b) Calculate the volume of the cone
Answers b) 199.5
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9. The diagram shows a square-based pyramid ABCDE.
Vertex E is vertically above X, the centre of the square base.
The height of the pyramid, EX, is 17 cm. EC = 19 cm.
(i) Show that the length of the base is 12 cm.
(ii) Calculate the volume of the pyramid
Answers i) ii) 816
10. The diagram shows a wooden bowl.
It is made in the shape of a large hemisphere with a
small hemisphere removed from the centre.
The diameter of the large hemisphere is 20 cm.
The width of the rim of the bowl is 2 cm.
(a) Show that the total surface area of
the bowl is 364rcm2
(b) The bowl is made from wood.
The mass of 1cm3 of the wood is 0.74 g.
Calculate the mass of the bowl.
Answers a) b) 756.4
11. a) A sphere has a volume of 2572 cm3 . Find the radius of the sphere.
b) Hence find the curved surface area of this hemisphere.
c) If the density of thesphere’s metel is 3.1 g/cm3. Calculate the total mass of 5 hemispheres.
