The circumference of a circle is 15 inches. Find the circumference of a circle having three times the area of the given circle.

Question

In this case, π (pi) = 3.1416 and round the answer to the nearest tenth.

Answer 1

Hi Carmilla F.,

Let's see if I can get you to the answer a bit faster.

The circumference of a circle scales proportionately to the radius. The area of a circle scales proportionately to the square of the radius.

Therefore, to make a circle of 3 times the area, you just need a radius of 3^0.5 times that of the original circle; the circumference will also be 3^0.5 times that of the original circle. Type =15*3^0.5 into Google, and get 25.98... out, round to 26.0 inches.

No need to back-solve to radii, in this case, and less chance for calculator entry errors!

-- Cheers, -- Mr. d.

Answer 2

To determine the area of a circle, you need to know the radius of the circle. The formula for calculating area of a circle is:

A = ¶ • r²

We can determine the radius of the circle in this problem by using the 15 inch circumference. The formula for the circumference of a circle is:

C= 2 • ¶ • r

15 = 2 • 3.1416 • r

15 = 6.2832 • r

15/6.2832 = 6.2832 • r / 6.2832

2.3873 inches = r

Now we can use this radius to find the area of the 15 inch circle:

A = 3.1416 • r²

A = 3.1416 • 2.3873²

A = 17.9046 inches²

To find the circumference of a circle with 3 times this area, we can multiply the area by 3 and then work "backward" to find the radius and circumference.

Three times area : A = 3 • 17.9046

A = 53.7138

Now using this area, we can determine the radius of the larger circle:

A = 3.1416 • r²

53.7138 = 3.1416 • r²

53.7138/3.1416 = 3.1416 • r² /3.1416

17.0976 = r²

4.134 inches = r

The circumference of the larger circle will be:

C = 2 • 3.1416 • r

C = 6.2832 • 4.134

C = 25.97

C = 26.0 inches rounded to the nearest tenth

Answer 3

To determine the area of a circle, you need to know the radius of the circle. The formula for calculating area of a circle is:

A = ¶ • r²

We can determine the radius of the circle in this problem by using the 15 inch circumference. The formula for the circumference of a circle is:

C= 2 • ¶ • r

15 = 2 • 3.1416 • r

15 = 6.2832 • r

15/6.2832 = 6.2832 • r / 6.2832

2.3873 inches = r

Now we can use this radius to find the area of the 15 inch circle:

A = 3.1416 • r²

A = 3.1416 • 2.3873²

A = 17.9046 inches²

To find the circumference of a circle with 3 times this area, we can multiply the area by 3 and then work "backward" to find the radius and circumference.

Three times area : A = 3 • 17.9046

A = 53.7138

Now using this area, we can determine the radius of the larger circle:

A = 3.1416 • r²

53.7138 = 3.1416 • r²

53.7138/3.1416 = 3.1416 • r² /3.1416

17.0976 = r²

4.134 inches = r

The circumference of the larger circle will be:

C = 2 • 3.1416 • r

C = 6.2832 • 4.134

C = 25.97

C = 26.0 inches rounded to the nearest tenth