Radio station KMA is increasing its radio listening radius from 40 miles to 50 miles. How many additional square miles of listening area, to the nearest tenth, will the radio station gain?

I thought it was 10 miles.But it says round.So im a little confused.If you could Help.I would be very happy.

the area of a circle is pi * r^2
if the first radius is 40 miles, then the area is pi*1600. the second radius is 50 miles, so the area is pi*2500. 2500(pi)-1600(pi)= 900(pi) additional sq miles of area. and then you multiply 900 and pi to get the answer.

To clarify, the question asks for the additional square miles of listening area that the radio station will gain when it increases its radio listening radius from 40 miles to 50 miles. You correctly determined that the formula for the area of a circle is pi * r^2, where r represents the radius.

First, you calculated the area of the circle with a 40-mile radius by substituting r = 40 into the formula, giving you pi * 40^2 = 1600(pi) square miles.

Then, you calculated the area of the circle with a 50-mile radius by substituting r = 50 into the formula, giving you pi * 50^2 = 2500(pi) square miles.

To find the additional square miles of listening area, you subtracted the area with a 40-mile radius from the area with a 50-mile radius. Therefore, 2500(pi) square miles - 1600(pi) square miles = 900(pi) square miles.

Since the question asks for the additional square miles of listening area to the nearest tenth, you would multiply 900(pi) by the numerical approximation of pi (approximately 3.14) to get the answer.

So, the radio station will gain approximately 2826 square miles (900 x 3.14 = 2826) of additional listening area when it increases its radius from 40 miles to 50 miles.