Question

A 3×10, rectangle sits inside a circle with radius of 12. What is the area of the shaded region? Round your final answer to the nearest hundredth.

Answer 1

422.39 square units.

Explanation:

We have been given that a 3×10, rectangle sits inside a circle with radius of 12. We are asked to find the area of shaded region.

The area of shaded region will be equal to the area of circle minus area of the rectangle.

`\text{Area of shaded region}=\text{Area of circle - Area of rectangle}`

`\text{Area of shaded region}=(\pi r^2)-l* h`, where,

r = Radius of circle,

l = Length of rectangle,

b = Height of rectangle.

Upon substituting our given values in above equation we will get,

`\text{Area of shaded region}=(\pi*12^2)-3* 10`

`\text{Area of shaded region}=144\pi-30`

`\text{Area of shaded region}=452.38934211693-30`

`\text{Area of shaded region}=422.38934211693\approx 422.39`

Therefore, the area of shaded region will be approximately 422.39 square units.

Answer 2

The area of the circle for this case is given by:

`A1 = \pi * r ^ 2`Where,
r: radius of the circle.
Substituting values we have:

`A1 = \pi * (12) ^ 2 A1 = 452.3893421`
The area of the rectangle is given by:

`A2 = (w) * (l)`
Where,
w: width
l: long
Substituting values we have:

`A2 = (3) * (10) A2 = 30`
The area of the shaded region is:

`A1 - A2 = 452.3893421 - 30 A1 - A2 = 422.3893421`
Rounding off we have:

`A1 - A2 = 422.39`
Answer:
The area of the shaded region is:
A1 - A2 = 422.39