Question

A square is circumscribed about a circle with an 8-inch radius, as shown below. What is the area, in square inches, of the region that is inside the square but outside the circle?

Choices:
16 − 64π

256−8π

64 −16 π

256 −64π

Answer 1

Option 4. 256 - 64π is the correct option.

Explanation:

In the given picture a square is circumscribed about a circle with a side = 2r

where r is the radius of the circle.

Therefore area of the square = (2r)² = 4r² = 4 × 8² = 4 × 64 = 256 in²

Now area of the circle = πr² = π × 8² = 64π in²

Now area of region that is inside the square and outside the circle =

Area of square - area of circle = (256 - 64π) in².

Therefore the answer is (256 - 64π).