The exclamation point (!) on a billboard consists of a circle sector and circle. The radius of the sector is 9 ft, and the radiu

Question

3 years ago

15

The exclamation point (!) on a billboard consists of a circle sector and circle. The radius of the sector is 9 ft, and the radiu

s of the circle is 1.5 ft. The angle of the sector is 24°. What is the total area of the exclamation point on the billboard? Round to the nearest tenth.

Mathematics

1 answer:

harina [27] · Answer 1 · 2022-02-17T22:30:40+03:00

Answer:

24.0 square feet

Step-by-step explanation:

The area of the sector is given by ...

A = (1/2)r²θ . . . . . where θ is the angle in radians

The area of the circle is the same, with θ=2π, so is ...

A = πr²

__

In this problem, the area of the sector is ...

A = (1/2)(9 ft)²(24π/180) = 27π/5 ft² ≈ 16.9646 ft²

The area of the circle is ...

A = π(1.5 ft)² = 9π/4 ft² ≈ 7.0686 ft²

Then the total area of the exclamation point is ...

16.9646 +7.0686 ≈ 24.0 . . . ft²

The area is about 24.0 square feet.