37.3k views
5 votes
The radius of a circle is 10 kilometers. What is the area of a sector bounded by a 90° arc? Give the exact answer in simplest form.

User Cmill
by
7.2k points

1 Answer

6 votes

The area of a sector of a circle is given by the formula:

A = (θ/360°) x πr²

where θ is the central angle of the sector in degrees and r is the radius of the circle.

In this case, the radius of the circle is given as 10 kilometers, and the central angle of the sector is 90°, so we can plug in these values to find the area of the sector:

A = (90°/360°) x π(10 km)²

A = (1/4) x π x 100 km²

A = (25/4)π km²

Therefore, the exact area of the sector bounded by a 90° arc of a circle with a radius of 10 kilometers is (25/4)π km², or approximately 19.63 km².

User Shabria
by
8.1k points

No related questions found