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kirill [66]
3 years ago
12

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

Mathematics
2 answers:
marissa [1.9K]3 years ago
7 0
2460.51

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

A≈ 2460.51
astraxan [27]3 years ago
4 0

Answer:

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

<h3>☯ Question :</h3>
  • Find the area of a circle that has a circumference of 175.84 inches.
<h3 /><h3>☯ Step - by - step explanation :</h3>

☄ 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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