Source: Complete International Mathematics For Cambridge IGCSE - David Rayner, Jim Fenson
1. Calculate the volume of the prisms. All lengths in cms.| a) |  |  |
| b) |  |  |
| c) |  |  |
| d) |  |  |
| e) |  |  |
2. Calculate volumes of following objects:
| a) | Sphere: Radius =10 cm |  |
| b) | Cone: Height = 5 cm Radius = 2 cm |  |
| c) | Cone: Height = x cm Radius = 2x cm |  |
| d) | Pyramid: Rectangular base Base = 7 cm by 8 cm Height = 5 cm |  |
| e) | Pyramid: Square base Base side = 4 m Height = 9 m |  |
| f) | Pyramid: Equilateral triangular base Base side = 8 cm Height = 10 cm |  |
| g) | Hemisphere: Radius = 5 cm |  |
3. Find the height of a cylinder of volume 200 cm³ and radius 4 cm.
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4.A cone is attached to a hemisphere of radius 4 cm.
If the total height of the object is 10 cm, find the volume.  |  |
5. When 3 liters of oil is removed from an upright cylindrical can, the level falls by 10 cm.
Find the radius of the can.
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6. A solid rectangular block of copper 5cm by 4 cm by 2 cm is drawn out to make
a cylindrical wire of diameter 2 mm. Calculate the length of the wire.
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7. Water flows from a hose-pipe of internal diameter 1 cm at a rate of 5 liters per minute.
At what speed is the water flowing through the pipe?
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8. A prism has volume 100 cm³ and length 8 cm.
If the cross-section is an equilateral triangle, find the length of the a side of the triangle.
9. A cylindrical tin of height 15 cm and radius 4 cm is filled with sand from a rectangular box.
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9. A cylindrical tin of height 15 cm and radius 4 cm is filled with sand from a rectangular box.
How many times can the tin be filled if the dimensions of the box are 50 cm x 40 cm x 20 cm.
10. Rain which falls onto a flat rectangular surface of length 6 m and width 4 m is collected in a
cylinder of internal radius 20 cm. what is the depth of water in the cylinder after a storm in
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10. Rain which falls onto a flat rectangular surface of length 6 m and width 4 m is collected in a
cylinder of internal radius 20 cm. what is the depth of water in the cylinder after a storm in
which 1 cm of rain fell?
| The volume of water collected can be calculated by working out the area of the flat rectangular surface multiplied by 1 cm of rainfall.  |
11.Six square based pyramids fit exactly onto the six faces of a cube of side 4 cm.
If the volume of the object formed is 256 cm³, find the height of each of the pyramids.
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12. A solid metal cube of side 6 cm is recast into a solid sphere.
Find the radius of the sphere.
| Solid metal cube is recast into a solid sphere. Hence Volume of cube will be same as that of sphere  |
13. A hollow spherical vessel has internal and external radii of 6 cm and 6.4 cm respectively.
Calculate the mass of the vessel if it is made of metal of density 10 g/ cm³
| The spherical vessel is hollow. Hence the volume of metal is that of the frame only. This can be calculated by subtracting the volume of the inner sphere from the volume of out sphere.   |