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Written below are some worked questions on how to find the area of a sector if you know the radius and the angle inside the sector.

Question 1

A sector has a radius of 3cm and an inside angle of 45⁰. Work out the area of the sector.

The area of a sector can be calculated by using the following formula:

Area of the sector = angle/360 × π × radius²

So all you need to do is substitute the radius which is 3 cm and the angle which is 45⁰ into this formula.

Area of a sector  = 45/360 × π × 3²

Now type this into you scientific calculator exactly how it appears above (use your fraction key).

Area of sector = 3.53 cm² to 3 significant figures.

Question 2

Another sector has a radius of 15 m and an inside angle of 135⁰. Work out the area of the sector.

Again, the area of a sector can be calculated by using the following formula:

Area of the sector = angle/360 × π × radius²

Next substitute the radius which is 15 m and the angle which is 135⁰ into this formula.

Area of a sector  = 135/360 × π × 15²

Now type this into you scientific calculator exactly how it appears above (use your fraction key).

Area of sector = 265.1 m² to 3 significant figures.

Question 3

A sector has a radius of 7.2 cm and an inside angle of 286⁰. Work out the area of the sector and round your final answer to the nearest integer.

Again, the area of a sector can be calculated by using the following formula:

Area of the sector = angle/360 × π × radius²

Next substitute the radius which is 7.2 cm and the angle which is 286⁰ into this formula.

Area of a sector  = 286/360 × π × 7.2²

Now type this into you scientific calculator exactly how it appears above (use your fraction key).

Area of sector = 129 cm² to the nearest integer.

Question 4

A sector has a radius of 9 mm and an inside angle of 11⁰. Work out the area of the sector and round your final answer to 3 decimal places.

Again, the area of a sector can be calculated by using the following formula:

Area of the sector = angle/360 × π × radius²

Next substitute the radius which is 9 mm and the angle which is 11⁰ into this formula.

Area of a sector  = 11/360 × π × 9²

Now type this into you scientific calculator exactly how it appears above (use your fraction key).

Area of sector = 7.775 mm² to 3 decimal places.

If you are still finding this difficult then read my other article on finding the area of a sector.

If you want some harder real life example on finding the area of a sector then click here.

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