Volume & Surface Area (Cambridge O Level Maths)

A container is made from a cylinder and a cone, each of radius 5 cm.
The height of the cylinder is 12 cm and the height of the cone is 4.8 cm.

The diagram shows a solid cylinder and a solid sphere.
The cylinder has radius and height .
The sphere has radius .

Find the volume of the sphere as a fraction of the volume of the cylinder.
Give your answer in its lowest terms.
[The volume, , of a sphere with radius  is  .]

The surface area of the sphere is 81 cm².
 
Find the curved surface area of the cylinder.
Give your answer in terms of .
[The surface area, , of a sphere with radius  is  .]
 

........................................... cm²

The diagram shows a container in the shape of a prism with an open top.
The cross-section of the prism, , is a trapezium.
, and .
The height of the container is .
The area of the cross-section is 

Calculate the capacity of the container in litres.

...................................... litres

Calculate the total surface area of the inside of the container.

......................................... cm²

The volume of a cuboid is 180 cm³.
The base is a square of side length 6 cm.
 
Calculate the height of this cuboid.
 

....................................... cm

A water tank in the shape of a cuboid has length 1.5 metres and width 1 metre.
The water in the tank is 60 centimetres deep.
 
Calculate the number of litres of water in the tank.
 

....................................... litres

The diagram shows a solid cuboid with base area 7 cm².
The volume of this cuboid is 21 cm³.

Work out the total surface area.

......................................... cm²

Find the volume of a cylinder of radius 5 cm and height 8 cm.
Give your answer in terms of .
Give the units of your answer.

A cube has side length cm. The volume of the cube is 1000 cm³.
 
Calculate the value of .
 

= ....................................................

A solid metal cone has radius 10 cm and height 36 cm.

Calculate the volume of this cone.
Give your answer in terms of .
[The volume, , of a cone with radius  and height  is  .]
 

......................................... cm³

The diagram below shows a solid circular cone and a solid sphere.

The cone has radius cm and height  cm.
The sphere has radius  cm.
The cone has the same total surface area as the sphere.

Show that  .

[The curved surface area, , of a cone with radius  and slant height  is .]
[The surface area, , of a sphere with radius  is .]

The diagram shows three solids.
The base radius of the cone is 6 cm and the slant height is 12 cm.

Show that the total surface area of the cone is 108 cm².
[The curved surface area, , of a cone with radius and slant height is .]

The radius of the sphere is cm and the radius of the hemisphere is cm.
The total surface area of each solid is the same.
  
Find the value of and the value of .
Give the value of  as a simplified surd.
[The surface area, , of a sphere with radius is .]

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