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If a circle’s circumference is 10π centimeters long, what is the area

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If a circle’s circumference is 10π centimeters long, what is the area [#permalink] New post   24 Mar 2020, 01:18
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If a circle’s circumference is \(10π\) centimeters long, what is the area of the circle, in square centimeters?

(A) \(12.5\)

(B) \(5π\)

(C) \(22.5\)

(D) \(25π\)

(E) \(10π\)
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Re: If a circle’s circumference is 10π centimeters long, what is the area [#permalink] New post   26 Mar 2020, 03:59
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We know:

Circumference = Distance (d) x π = 10π

Radius = Distance / 2 = 10/2 = 5

Area = A = π x r^2 = π x 5^2 = 25π

Correct Answer:

D
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Re: If a circle’s circumference is 10π centimeters long, what is the area [#permalink] New post   26 Mar 2020, 10:49
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Solution



Given
In this question, we are given that
    • A circle’s circumference is \(10π\) centimeters long

To find
We need to determine
    • The area of the circle, in square centimeters

Approach and Working out
If we assume the radius of the circle to be R cm, then we can write
    • \(2πR = 10π\)
    Or, \(R = 5\) cm

Hence, the area of the circle = \(πR^2 = π(5)^2 = 25π\) square cm

Thus, option D is the correct answer.

Correct Answer: Option D
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Re: If a circle’s circumference is 10π centimeters long, what is the area [#permalink] New post   26 Mar 2020, 12:02
SajjadAhmad wrote:
If a circle’s circumference is \(10π\) centimeters long, what is the area of the circle, in square centimeters?

(A) \(12.5\)

(B) \(5π\)

(C) \(22.5\)

(D) \(25π\)

(E) \(10π\)


The formula for the circumference of a circle is C = 2πr.

10π = 2π(r)
r = 5

The formula for a circle is A = πr^2

A = π(5)^2
A = 25π

The answer is (D).
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Re: If a circle’s circumference is 10π centimeters long, what is the area [#permalink] New post   29 Mar 2020, 05:03
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SajjadAhmad wrote:
If a circle’s circumference is \(10π\) centimeters long, what is the area of the circle, in square centimeters?

(A) \(12.5\)

(B) \(5π\)

(C) \(22.5\)

(D) \(25π\)

(E) \(10π\)


Use the circumference formula: C = 2πr

10π = 2πr

5 = r

Now use the area formula: A = πr^2

A = π25 = 25π

The area is 25π square centimeters.

Answer: D
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Re: If a circle’s circumference is 10π centimeters long, what is the area [#permalink]
29 Mar 2020, 05:03
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