Question

What is the area of the shaded portion of the circle?

Answer 1

The angle between the lines in 90 degrees so the area of the  whole sector is 1/4 of a circle

= 1/4 * pi * 8^2

The area of the triangle = 1/2 * 8 * 8 = 32

so area of the shaded segment =  (16pi - 32) in^2

choice 1.

Answer 2

Answer:

the answer is the first option

$(16\pi\ -32)\ in^{2}$

Step-by-step explanation:

we know that

The area of the shaded portion of the circle is equal to the area of a quarter circle minus the area of the right triangle

Step 1

Find the area of a quarter circle

$A=\frac{1}{4}\pi r^{2}$

we have

$r=8\ in$

substitute

$A=\frac{1}{4}\pi (8)^{2}=16\pi\ in^{2}$

Step 2

Find the area of the right triangle

we know that

the area of the triangle is equal to

$A=\frac{1}{2}bh$

in this problem we have

$b=h=8\ in$

substitute

$A=\frac{1}{2}(8)^{2}=32\ in^{2}$

Step 3

Find the area of the shaded portion

Remember that

The area of the shaded portion of the circle is equal to the area of a quarter circle minus the area of the right triangle

$A=(16\pi\ -32)\ in^{2}$