Question

What is the area of a sector with a central angle of 60° and a radius of 16.7 ft?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

ft²

Answer 1

145.95ft²

Explanation:

A "sector" is a piece of a circle like a pie slice.

If the central angle is 60° and a whole circle is 360°, then the piece of the circle we are looking at is

60/360, or 1/6 of the circle.

We can find the area of the whole circle, then divide by 6.

Area_wholecircle

= πr²

= 3.14×16.7²

= 3.14×278.88

= 875.7146

Now divide by 6 (same as times by 1/6 and less stressful) to find the area of the sector.

Area_sector

= 875.7146/6

= 145.95243333

Round to hundredths (two decimal places)

~= 145.95

The area of the sector is 145.95ft².