A circle has a sector with area \dfrac{24}{5}\pi 5 24 πstart fraction, 24, divided by, 5, end fraction, pi and central angle of \purple{48^\circ}48 ∘ start color #9d38bd, 48, degrees, end color #9d38bd. What is the area of the circle?

Question:

A circle has a sector with area 24π/5 and central angle of 48°.

What is the area of the circle?

The area of the circle is 36π

Step-by-step explanation:

Given

Area of sector = 24π/5

Central angle, θ = 48°

Required:

Area of the circle

First we need to calculate radius of the circle.

This can be solved from area of a sector

Area of a sector = θ *

By substituting 24π/5 for area and 48° for θ, we have

Multiply both sides by

36π = πr²

Divide both sides by π

36 = r²

Take square root of both sides

√36 = √r²

6 = r

Hence, radius = 6

Then, the area of the circle can now be calculated.

Area = πr²

Substitute 6 for r

Area = π * 6²

Area = π * 36

Area = 36π

Hence, the area of the circle is 36π