Did you know?

We also have Bitesize study guides covering many subjects at National 4 and National 5 on our Knowledge & Learning BETA website.

Home > Maths II > Relationships > Changing the subject of a formula

Maths II

Changing the subject of a formula

Sometimes we will need to rearrange a formula to find the value of a subject.

For instance, we may know the area of a circle and need to find the radius. To do this, rearrange the formula to make the radius the subject.

Changing the subject of a formula

The area of a circle (A) is \pi r^2

So A = \pi r^2

If we know the radius, it is easy to find the area using this formula. However, if we know the area and want to find the radius, rearrange the formula to make 'r' the subject.

A = \pi r^2

[Start, by dividing both sides by \pi]

{A \over \pi} = r^2

[Then take the square root of both sides]

\sqrt{A \over \pi} = r or r = \sqrt{A \over \pi}

Question

The formula connecting ºC and ºF is -

C = {{5(F - 32)} \over 9}

Rearrange the formula to make 'F' the subject.

Answer

C = {{5(F - 32)} \over 9}

[Multiply by 9] 9C = 5(F - 32)

[Divide by 5] {9C \over 5} = F - 32

[Add 32] {9C \over 5} + 32 = F

So F = {9C \over 5} + 32

Note: {(9C + 160)} \over 5 is also correct.

Question

The formula for the volume (V) of a sphere is V = {4 \over 3} \pi r^3

Rearrange the formula to make 'r' the subject.

Answer

V = {4 \over 3} \pi r^3

[Multiply both sides by 3] 3V = 4 \pi r^3

[Divide by 4 \pi]{3V \over 4 \pi} = r^3

[Take the cube root of both sides]

\sqrt[3] {3V \over 4 \pi} = r or r = \sqrt[3] {3V \over 4 \pi}

BBC navigation

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.