Question

A circular pen has an area of 64
`\pi` square yards. What is the circumference of the pen.

I need help.

Answer 1

What we know:
shape is circular
Area=64π yr²
Area=πr²
circumference=2πr

In order to find circumference we need r=radius. We can use the area to find r by solving for r using substitution of the information we know above.

Area=πr²
64π=πr² substitution
64π/π=π/πr² multiplicative inverse
64=r²
√64=√r² properties of radicals
8=r We would get two solutions, a positive and negative one but we will only use the positive solution since radius is positive

Circumference=2πr
C=2π(8)=16π yards

Answer 2

The answer would be 16π. We can derive this answer by first recalling the formulas for the Area and Circumference of a circle. Here are the formulas:
A = πr²
C = 2πr
Now that we have listed our necessary formulas together, we can use our given information to get our circumference. First off, we can substitute the Area to be 64π, or A = π(64). When we look at the formula for the area, we see that 64 takes place of r². This means that we need to take the square root of 64, which is 8. Since we have found the value of r, we can substitute the value we got into the circumference formula. Hence, we get 2π(8), and when we simplify that down, we get C = 16π. Hope this helped and have a phenomenal day!