Math  /  Geometry

QuestionThe circumference of a circle is 18π cm18 \pi \mathrm{~cm}. What is the area, in square centimeters? Express you answer in terms of π\pi.
Answer Attempt 3 out of 5 A=A= \square cm2\mathrm{cm}^{2}
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Studdy Solution

STEP 1

1. The circle's circumference is given as 18π 18\pi cm.
2. The area needs to be expressed in terms of π\pi.

STEP 2

1. Recall the formula for the circumference of a circle.
2. Use the circumference to find the radius.
3. Recall the formula for the area of a circle.
4. Substitute the radius into the area formula.
5. Calculate the area.

STEP 3

Recall the formula for the circumference of a circle:
C=2πr C = 2\pi r
where C C is the circumference and r r is the radius.

STEP 4

Use the given circumference to find the radius:
18π=2πr 18\pi = 2\pi r
Divide both sides by 2π 2\pi :
r=18π2π=9 r = \frac{18\pi}{2\pi} = 9

STEP 5

Recall the formula for the area of a circle:
A=πr2 A = \pi r^2

STEP 6

Substitute the radius into the area formula:
A=π(9)2 A = \pi (9)^2

STEP 7

Calculate the area:
A=π×81 A = \pi \times 81 A=81π A = 81\pi
The area of the circle is:
81π cm2 \boxed{81\pi \text{ cm}^2}

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