Question

Find the area of a circle that has a circumference of 175.84 inches

Answer 1

2460.51

A = c^2/4pi
175.84^2/4pi

A≈ 2460.51

Answer 2

Answer:

${ \boxed{ \bold{ \text{Area \: of \: a \: circle} \: = \tt{2461.76 \: {inches}^{2}}}}}$

☯ Question :

• Find the area of a circle that has a circumference of 175.84 inches.

☯ Step - by - step explanation :

☄ 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

⟶ $\sf{2\pi \: r \: = 175.84}$

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

And we're done !

Hope I helped!

Have a wonderful time!ツ

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