Question

Find the area of a sector with a central angle of 2pi/15 and a radius of 18.8 m

Answer 1

Answer:

74.02 square meters.

Step-by-step explanation:

We are asked to find the area of sector of circle, whose central angle is $\frac{2\pi}{15}$.

We will use area of sector formula to solve our given problem.

$\text{Area of sector}=\frac{\theta}{2\pi}\times \pi r^2$, where, r represents radius of circle.

Upon substituting our given values in above formula, we will get:

$\text{Area of sector}=\frac{\frac{2\pi}{15}}{2\pi}\times \pi (18.8)^2$

Using fraction rule $\frac{\frac{a}{b}}{c}=\frac{a}{bc}$, we will get:

$\text{Area of sector}=\frac{2\pi}{15\times 2\pi}\times \pi (18.8)^2$  

$\text{Area of sector}=\frac{1}{15}\times \pi \times 353.44$  

$\text{Area of sector}=23.5626666\times \pi$  

$\text{Area of sector}=74.0243004\approx 74.02$  

Therefore, the area of given sector of circle is 74.02 square meters.

Answer 2

We know that
[Area of a circumference]=pi*r²
for r=18.8 m
Area=pi*18.8²=1109.80 m²

if the area for 2pi radians (full circumference) is --------------> 1109.80 m²
                  for 2pi/15----------------------------------> X
X=(2pi/15)*1109.80/2pi----------> 73.99 

the answer is 73.99 m²