Question

A circle with radius 5 has a sector with a central angle of 9/10 pi

radians.

What is the area of the sector?

Either enter an exact answer in terms of it or use 3.14 for and enter your answer as a decimal rounded to the

nearest hundredth.

Answer 1

Answer:

35.33

Step-by-step explanation:

The circle with radius 5 has a sector with a central angle of 9/10 pi.

The area of a sector is given as:

$A_s = \frac{\alpha }{2\pi} * \pi r^2$

where α = central angle of the sector in radians

r = radius of the circle

The area of the sector is therefore:

$A_s = \frac{\frac{9 \pi}{10} }{2 \pi} * (3.14 * 5^2)\\ \\A_s = \frac{9}{20} * 78.5\\\\A_s = 35.33$

The area of the sector is 35.33.

Answer 2

Answer:

The area of the sector to nearest hundredth is 35.33

Step-by-step explanation:

Formula for calculating the area of a sector is given as $\frac{\theta}{360} *\pi r^{2}$ where;

r is the radius of the circle

theta is the angle substended by the sector.

Given r = 5 and central angle theta = $\frac{9 \pi}{10}$

Area of the sector is expressed as shown;

$= \frac{9\pi/10}{2\pi}*\pi (5)^{2} \\= \frac{9\pi}{20\pi}*25\pi\\ = \frac{225\pi}{20} \\= 225*3.14/20\\= 35.33$

The area of the sector to nearest hundredth is 35.33