Question

Compute the area of a circle with a circumference of 56 pi feet - include the formula, exact answer, and Approximate Answer. PLEASE HELP!!!

Answer 1

Answer : Exact answer of area of circle= 2464 feet

Approximate answer of area of circle = 2461.76 feet

Step-by-step explanation:

We have given that,

Circumference of a circle=56
`\pi` feet

And we know that,

Cirumference of a circle= 2
`\pi`r

So,

For exact answer we take the value of
`\pi` =
`(22)/(7)`,

Now, 2
`\pi`r= 56
`\pi` feet, where r is a radius

⇒r=
`(56\pi)/(2\pi )`

⇒r= 28 feet

Now we will use the formula for the area of circle,

Area of circle=
`\pi`r²

=
`(22)/(7)`×28×28

=
`(17248)/(7)`

=2464 feet

So, the exact answer will be 2464 feet.

Now ,we do for approximate value, we will use the value of
`\pi`=3.14

Circumference of circle = 56
`\pi` feet

= 56 × 3.14 feet

= 175.84 feet

So we use the formula of circumference again which is 2
`\pi`r

∴ 2
`\pi`r= 175.84

⇒2× 3.14× r= 175.84

⇒6.28 × r= 175.84

⇒ r=
`(175.84)/(6.28)`

⇒ r=28 feet

Now, Area of circle=
`\pi` r²

=3.14×28×28 feet

=2461.76 feet

Hence , Area of circle in both the cases will be 2464 feet and 2461.76 feet respectively.