A circle has an area of 45 square meters. What is the area of a sector with an arc measure of 70°?

THe area of the arc is 8.75 m²

Step-by-step explanation:

In order to calculate the are of the sector we need to know the radius of the circle. For that we can use the formula for the area of the circle, which is shown below:

area circle = pi*r²

Applying the data from the problem, we have:

45 = pi*r²

pi*r² = 45

r² = 45/pi

r = sqrt (45/pi) = 3.7846 m

Therefore the area of the arc is:

arc's area = angle*pi*r²/360

arc's area = 70*pi * (45/pi) / 360 = 70*45/360 = 8.75 m²

THe area of the arc is 8.75 m²