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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]

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24 Mar 2020, 00:18
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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]

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26 Mar 2020, 02:59
1
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

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Re: If a circle’s circumference is 10π centimeters long, what is the area  [#permalink]

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26 Mar 2020, 09:49
1

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.

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Re: If a circle’s circumference is 10π centimeters long, what is the area  [#permalink]

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26 Mar 2020, 11:02
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

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Re: If a circle’s circumference is 10π centimeters long, what is the area  [#permalink]

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29 Mar 2020, 04:03
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.

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Re: If a circle’s circumference is 10π centimeters long, what is the area   [#permalink] 29 Mar 2020, 04:03