Spheres and Cones worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

1. 2 marks

   Here is a solid sphere of radius \(11\) cm.

   Surface area of a sphere \(= 4\pi r^2\)

   Find the surface area of the sphere. Give your answer in terms of \(\pi\).

2. 3 marks

   The diagram shows a solid sphere. The diameter of the sphere is \(24\) cm.

   Volume of a sphere \(= \frac{4}{3}\pi r^3\)

   Calculate the volume of the sphere. Give your answer to 1 decimal place.

3. 5 marks

   A solid plastic ball is a sphere of radius \(12\) cm.

   The ball is cut exactly in half through its centre, making two identical solid hemispheres.

   Volume of a sphere \(= \frac{4}{3}\pi r^3\)

   Surface area of a sphere \(= 4\pi r^2\)

   (a)

   Find the volume of one of the hemispheres. Give your answer in terms of \(\pi\).

   (b)

   Find the total surface area of one of the hemispheres. Give your answer in terms of \(\pi\).

4. 5 marks

   Here is a solid cone. The radius of its base is \(9\) cm and its slant height is \(15\) cm.

   Volume of a cone \(= \frac{1}{3}\pi r^2 h\)

   (a)

   Calculate the vertical height \(h\) of the cone.

   (b)

   Calculate the volume of the cone. Give your answer in terms of \(\pi\).

5. 3 marks

   Here is a solid cone with base radius \(12\) cm and slant height \(20\) cm.

   Curved surface area of a cone \(= \pi r l\), where \(l\) is the slant height.

   Calculate the total surface area of the cone. Give your answer in terms of \(\pi\).

6. 4 marks

   A model of a water tower at a village is made from a cylinder with a hemisphere joined to the top of it.

   The cylinder and the hemisphere both have a radius of \(3\) cm. The cylinder has a height of \(24\) cm.

   Volume of a sphere \(= \frac{4}{3}\pi r^3\)

   Work out the total volume of the model. Give your answer in terms of \(\pi\).

7. 2 marks

   The diagram shows a solid sphere of radius \(10\) cm.

   Surface area of a sphere \(= 4\pi r^2\)

   Work out the surface area of the sphere. Give your answer in terms of \(\pi\).

8. 3 marks

   Here is a solid sphere. The diameter of the sphere is \(16\) cm.

   Volume of a sphere \(= \frac{4}{3}\pi r^3\)

   Work out the volume of the sphere. Give your answer to 1 decimal place.

9. 5 marks

   A solid wooden ball is a sphere of radius \(12\) cm.

   The ball is cut exactly in half through its centre, making two identical solid hemispheres.

   Volume of a sphere \(= \frac{4}{3}\pi r^3\)

   Surface area of a sphere \(= 4\pi r^2\)

   (a)

   Find the volume of one of the hemispheres. Give your answer in terms of \(\pi\).

   (b)

   Find the total surface area of one of the hemispheres. Give your answer in terms of \(\pi\).

10. 5 marks

    The diagram shows a solid cone. The radius of its base is \(7\) cm and its slant height is \(25\) cm.

    Volume of a cone \(= \frac{1}{3}\pi r^2 h\)

    (a)

    Find the vertical height \(h\) of the cone.

    (b)

    Find the volume of the cone. Give your answer in terms of \(\pi\).

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