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Given the circumference of a circle is 8π centimeters, calculate the area of the circle in terms of π.

User Panktijk
by
8.0k points

2 Answers

11 votes

Answer:

16π cm²

Explanation:

circumference = 2πr

Area = πr²

We need to determine r to calculate the area

2πr = 8π

Divide both sides of the equation by 2π to find r

r = 4

Now, we determine area.

area = πr² = π4² = 16πcm²

User Gdm
by
8.1k points
7 votes

Answer:


  • \Large\boxed{\sf{16\pi\text{cm}^2}}

Explanation:

The formula for the circumference of a circle can be used to solve this problem.


\underline{\text{CIRCLE OF A CIRCUMFERENCE FORMULA:}}


:\Longrightarrow: \sf{C=2\pi r}


\text{AREA:}= \sf{\pi r^2}


\sf{2\pi r=8 \pi}

You have to divide by 2 from both sides.


\sf{(2\pi r )/(2)=(8\pi)/(2) }

Solve.

Divde the numbers from left to right.

8/2=4

r=4


\sf{\pi r^2=\pi4^2}

Solve by exponents.


\sf{4^2=4*4=\boxed{\sf{16}}


\Longrightarrow: \boxed{\sf{16\pi \text{cm}^2}}

  • Therefore, the correct answer is 16πcm².

I hope this helps. Let me know if you have any questions.

User Shawon
by
7.6k points
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