3-Dimensional Solids

In this page, we will look at finding the volume and surface area of three-dimensional solids. The formulae for these solids can all be found in the formula booklet. You just need to know where to find them, as some are in the prior learning section and some are in the geometry and trigonometry section.


Key Concepts

On this page, you should learn about volumes and surface areas of

  • pyramids
  • cones
  • spheres
  • hemispheres

Summary

Test Yourself

Here is a quiz that practises the skills from this page


START QUIZ!

Exam-style Questions

Question 1

A glass is made up of a hemisphere and a cone.

Find the volume of the glass.

Give your answer to 3 significant figures


Hint

Full Solution

 

Question 2

The total surface area of a hemisphere is 1360 cm²

Find the radius.

Give your answer to 3 significant figures.


Hint

Full Solution

 

Question 3

a) A sphere has a radius of 10cm. Find the volume, giving your answer in terms of \(\large \pi\).

b) A cone has the same volume and the same radius as the sphere. Find the height of the cone.

c) Another sphere and cone have the same volume and the same radius, r. Find an equation for the height of the cone, h in terms of r.

Hint

Full Solution

 

Question 4

Three metal spheres have radii 1cm, 6cm and 8cm.

The spheres are melted down and made into one bigger sphere.

What is the radius of the single sphere?

Hint

Full Solution

 

Question 5

A cylindrical metal bar with height 12cm and diameter 12cm is melted down and made into spheres of diameter 3cm.

How many spheres will it make?

Hint

Full Solution

 

Question 6

A solid is made up of a cone and a cylinder.

The radius is 5cm, the height of the cone is 12cm and the height of the cylinder is 15cm.

Show that the total surface area of the solid is \(\large 240\pi\)


Hint

Full Solution

 

MY PROGRESS

How much of 3-Dimensional Solids have you understood?