Question

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

Answer 1

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

Answer 2

• 
  `\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.