Question

A circle with radius 16 centimeters is inscribed in a square.Which is the area of the shaded region? A. 804.25 square feet B. 1024 square feet C. 822.94 square feet D. 220.16 square feet

Answer 1

Answer:

Area of shaded region = 220.16 ft²

Explanation:

The diagram associated with this question is shown in the attached image

Unit in diagram is ft, so I'll use this unit in the answer

We are given that a circle with radius 16 ft is inscribed in a square

We know that the radius of an inscribed circle in a square is equivalent to half the length of the side of the square

This means that:

side length of the square = 2 × radius = 2 × 16 = 32 ft

From the diagram, we can note that:

area of shaded region = area of square - area of circle .............> equation I

1- getting area of square:

Area of a square is the square of its side length

This means that:

Area of square = (32)² = 1024 ft²

2- getting the area of the circle:

Area of circle = πr² = 3.14 × (16)² = 803.84 ft²

3- getting area of shaded region:

Use equation I

area of shaded region = area of square - area of circle

area of shaded region = 1024 - 803.84 = 220.16 ft²

Hope this helps :)