Question

12

Answer 1

A circle is characterized by radius, arc, sectors and circumference

• The length of the major arc is $18.75\pi$
• The radius of the circle is 15
• The area of the shaded sector is $140.625 * \pi$

Length of the major arc

The given parameters are:

$C = 30\pi$ --- the circumference

$\theta = 225^o$ -- the center angle

The length of the major arc is calculated using:

$L = \frac{\theta}{360} * C$

So, we have:

$L = \frac{225}{360} *30\pi$

Evaluate

$L = 18.75\pi$

Hence, the length of the major arc is $18.75\pi$

The radius of the circle

The circumference is given as:

$C = 30\pi$

So, we have:

$2\pi r = 30\pi$

Divide through by 2pi

$r = 15$

Hence, the radius of the circle is 15

The area of the shaded sector

The area of a sector is:

$A = \frac{\theta}{360} * \pi r^2$

So, we have:

$A = \frac{225}{360} * \pi * 15^2$

Evaluate

$A = 140.625 * \pi$

Hence, the area of the shaded sector is $140.625 * \pi$

Read more about circumference at:

brainly.com/question/15673093