# Math Help: How to Calculate the Area of Circle and Get an Answer in Terms of Pi

In this hub I will show you how to find the area of circle giving your answer in terms of Pi (π).

First of all you need to remember the formula for calculating the area of a circle:

A = πr²

A stands for area, π stands for Pi and r is the radius of
the circle (the distance halfway across).

**Example 1**

Work out the area of circle that has a radius of 7m, giving your answer in terms of Pi.

All you need to do is substitute r = 7 into A = πr²

A = πr²

= π × 7²

Since 7² = 49 (since 7 × 7 = 49) then you have:

= π × 49.

= 49π

So the final answer is 49π m² (put the number before Pi)

**Example 2**

Work out the area of circle that has a diameter of 22cm, giving your answer in terms of Pi.

This time the diameter is given (the distance all the way across) so you need to halve this to give the radius. Therefore, plug in r = 11 into A = πr²

A = πr²

= π × 11²

Since 11² = 121 (since 11 × 11 = 121) then you have:

= π × 121.

= 121π

So the final answer is 121π cm² (put the number before Pi)

**Example 3**

Work out the area of this circular lawn giving your answer in terms of Pi.

The radius of this lawn is 13m so you need to put this value into the formula.

A = πr²

= π × 13²

Since 13² = 169 (since 13 × 13 = 169) then you have:

= π × 169.

= 169π

So the final answer is 169π m² (put the number before Pi)

## Questions & Answers

What is the perimeter of a semi-circle with diameter of 86cm? Write the answer as an expression in terms of π?

First multiply the diameter by Pi to give 86π.

Next half 86π to give 43π (this is the arc length).

Next add on the diameter to give a final expression of 43π + 86.

Helpful 3Can you work out the perimeter of a semicircle with a radius of 3cm? Give your answer in terms of pi?

To work out the cirumference multiply the diameter by pi.

The diameter is 6, and so 6 multiplied by Pi is 6Pi.

You can leave the answer as 6Pi and the question is asking for an exact answer and not a decimal answer.

Helpful 17The circumference of a circle is 18π inches, so what is the area in terms with π?

Divide the 18π by π to give the diameter of the circle which gives 18.

Half 18 to give a radius of 9.

Now use πr^2 to give the area which comes to 81π .

Helpful 11Can you work out the area of a semicircle with a radius 3cm?

Square the radius to give 9.

Multiply by Pi to give 28.274...

Now divide this answer by 2 to give 14.1cm^2 rounded to 1 decimal place.

(Divide by 2 because a semicircle is half the area of a circle.)

Helpful 7A circle has circumference 27cm. What is the area of the circle? (use 3.14 for pi)

First divide the circumference by Pi to give the diameter of the circle (27 divided by 3.14 = 8.59...).

Now halve the diameter to give the radius (8.59 divided by 2 is 4.29...).

Now use Pi*r^2 to find the area of the circle (Pi times 4.29^2 = 58.0 cm^2 to 1 decimal place).

Helpful 5

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