Question

Find the area of a circle that has a circumference of 175.84 inches
with explanation.​

Answer 1

☄ Given :

Circumference of a circle = 175.84 inches

☄ To find :

Area of a circle = ?

☄ First, we have to find :

Radius of a circle ( r )

★ Finding the radius of a circle :

$\boxed{\sf{Circumference\:of\:a\:circle=2\pi\:r}}$

Substitute the value of circumference of a circle,

$\longrightarrow{\sf{175.84=2\pi\:r}}$

Swap the sides of the equation,

$\longrightarrow{\sf{2\pi\:r\:=175.84}}$

Use $\sf{\pi\:≈\:3.14}$,we obtain

$\longrightarrow{\sf{2\times\:3.14\times\:r=175.84}}$

Multiply : 2 by 3.14,

$\longrightarrow{\sf{6.28\:r=175.84}}$

Divide both sides by 6.28,

$\longrightarrow{\sf{\frac{6.28\:r}{6.28}=\frac{175.84}{6.28}}}$

$\longrightarrow{\sf{r\:=\:28\:inches}}$

☞ Now , we have :

• Radius of a circle (r)=28 inches

Finding the area of a circle having the radius of 28 inches:

$\boxed{\sf{Area\:of\:a\:circle=\pi\:{r}^{2}}}$

Substituting the radius , we get :

$\longrightarrow{\sf{Area\:of\:a\:circle=\pi\:{(28)}{2}}}$

$\longrightarrow{\sf{Area\:of\:a\:circle=784\:\pi}}$

Using $\sf{\pi\:≈\:3.14}$,we obtain:

$\longrightarrow{\sf{Area\:of\:a\:circle=784\times\:3.14}}$

$\longrightarrow{\boxed{\sf{Area\:of\:a\:circle=2461.76\:{inches}^{2}}}}$

Therefore, area of a circle is 2461.76 inches².