Practice Sector Area in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The area of a 'pie slice' region of a circle, bounded by two radii and the arc between them.

Imagine cutting a pizza into slices. Each slice is a sector. If you cut the pizza into 4 equal slices (90° each), each slice has \frac{1}{4} of the pizza's total area. The sector area is simply the fraction of the full circle determined by the central angle, applied to the total area.

Example 1

easy
Find the area of a sector of a circle with radius 8 cm and central angle 90°.

Example 2

medium
A sector has a central angle of \frac{2\pi}{3} radians and a radius of 9 cm. Find its area.

Example 3

easy
A pizza slice (sector) has a radius of 12 inches and a central angle of 45°. Find the area of the slice.

Example 4

hard
A sprinkler rotates through an angle of 120° and waters grass up to a radius of 15 ft. What area of grass does it water? If the water only reaches between 10 ft and 15 ft from the sprinkler, what annular sector area gets watered?
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