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[tex]\pi[/tex] feet
And we know that,
Cirumference of a circle= 2[tex]\pi[/tex]r
So,
For exact answer we take the value of [tex]\pi[/tex] = [tex]\frac{22}{7}[/tex],
Now, 2[tex]\pi[/tex]r= 56[tex]\pi[/tex] feet, where r is a radius
⇒r=[tex]\frac{56\pi}{2\pi }[/tex]
⇒r= 28 feet
Now we will use the formula for the area of circle,
Area of circle= [tex]\pi[/tex]r²
= [tex]\frac{22}{7}[/tex]×28×28
=[tex]\frac{17248}{7}[/tex]
=2464 feet
So, the exact answer will be 2464 feet.
Now ,we do for approximate value, we will use the value of [tex]\pi[/tex]=3.14
Circumference of circle = 56[tex]\pi[/tex] feet
= 56 × 3.14 feet
= 175.84 feet
So we use the formula of circumference again which is 2[tex]\pi[/tex]r
∴ 2[tex]\pi[/tex]r= 175.84
⇒2× 3.14× r= 175.84
⇒6.28 × r= 175.84
⇒ r= [tex]\frac{175.84}{6.28}[/tex]
⇒ r=28 feet
Now, Area of circle= [tex]\pi[/tex] 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.
