A rectangle measures 6 meters by 10 meters. Drawn on each side of the rectangle is a semicircle that has the endpoints of its diameter on the vertices of the rectangle. What percent larger is the area of the large semicircles than the area of the small semicircles? Express your answer to the nearest whole number.

I don't really understand how to draw the diagram and how to get the answer. please help

helloimnewperson Apr 26, 2019

#1**+2 **

We will have two semi-circles with a radius of 5 and two semi-circles of radius = 3

So....in effect.....we have one circle with a radius of 5 and one circle with a radius of 3

So.....

Area of Larger circle / Area of Smaller circle = pi *(5)^2 / [ pi * (3)^2] = 25 / 9

So....

[ (25/ 9) - 1 ] *100% = [16/9] * 100% ≈ 1.77 * 100% = 177% larger

To see this....note that an area of 18 would be 100% larger and an area of 27 would be 200% larger....25 is somewhere between these.....namely, 177%

CPhill Apr 26, 2019

#2**+1 **

*A rectangle measures 6 meters by 10 meters. Drawn on each side of the rectangle is a semicircle that has the endpoints of its diameter on the vertices of the rectangle. What percent larger is the area of the large semicircles than the area of the small semicircles? Express your answer to the nearest whole number.*

*I don't really understand.*

Think of it it as follows:

You have two semicircles diameter 10 which is the same as one whole circle diameter 10.

You have two semicircles diameter 6 which is the same as one whole circle diameter 6.

How much bigger is the area of the large circle than the area of the smaller circle?

The rectangle has nothing to do with it except to tell you what the diameters of the semicircles are.

You really don't even have to figure out the areas, since pi would cancel out anyway.

The question is, by what percentage is 5^{2} larger than 3^{2}

Dang it CPhill you beat me to the answer again LOL.

.

Guest Apr 26, 2019

edited by
Guest
Apr 26, 2019