Question

The radius of a circle is 4 feet. What is the area of a sector bounded by a 45° arc?

Answer 1

Answer:

$Area = 6.28\ ft^2$ or $Area = 2 \pi\ ft^2$

Step-by-step explanation:

Given

$Radius, r = 4ft$

$Angle, \theta = 45$

Required

Calculate the area of the sector

When angle is given in degrees, the area of sector is calculated as thus;

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

$Substitute\ r = 4\ and\ \theta = 45$

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

$Area = \frac{45}{360} * \pi * 4^2$

$Area = \frac{45}{360} * \pi * 16$

$Area = \frac{45*16}{360} * \pi$

$Area = \frac{720}{360} * \pi$

$Area = 2 * \pi$

$Area = 2 \pi\ ft^2$

The above is the area in terms of π

Solving further.... (Take π as 3.14)

$Area = 2 \pi\ ft^2$ becomes

$Area = 2 * 3.14\ ft^2$

$Area = 6.28\ ft^2$

Hence, the area of the sector is

$Area = 6.28\ ft^2$ or $Area = 2 \pi\ ft^2$