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

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  $\pi$ = $\frac{22}{7}$,

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

⇒r=$\frac{56\pi}{2\pi }$

⇒r= 28 feet

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

Area of circle= $\pi$r²

                     = $\frac{22}{7}$×28×28

                     =$\frac{17248}{7}$

                     =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= $\frac{175.84}{6.28}$

⇒ 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.