Answer:
[tex]{ \boxed{ \bold{ \text{Area \: of \: a \: circle} \: = \tt{2461.76 \: {inches}^{2}}}}} [/tex]
☯ 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 :
☄ First, we have to find :
♨ Finding the radius of a circle :
[tex] \boxed{ \sf{Circumference \: of \: a \: circle = 2\pi \: r}}[/tex]
Substitute the value of circumference of a circle
[tex] \longrightarrow{ \sf{175.84 = 2\pi \: r}}[/tex]
Swap the sides of the equation
⟶ [tex] \sf{2\pi \: r \: = 175.84}[/tex]
Use [tex] \sf{ \pi \: ≈ \: 3.14}[/tex] , we obtain
[tex] \longrightarrow{ \sf{2 \times 3.14 \times r = 175.84}}[/tex]
Multiply : 2 by 3.14
[tex] \longrightarrow{ \sf{6.28 \: r = 175.84}}[/tex]
Divide both sides by 6.28
[tex] \longrightarrow{ \sf{ \frac{6.28 \: r}{6.28} = \frac{175.84}{6.28}}} [/tex]
[tex] \longrightarrow{ \sf{r \: = \: 28 \: inches}}[/tex]
☞ Now , we have :
- Radius of a circle ( r ) = 28 inches
Finding the area of a circle having the radius of 28 inches :
[tex] \boxed{ \sf{Area \: of \: a \: circle = \pi \: {r}^{2} }}[/tex]
Substituting the radius , we get :
[tex] \longrightarrow{ \sf{Area \: of \: a \: circle = \pi \: {(28)}^{2} }}[/tex]
[tex] \longrightarrow{ \sf{Area \: of \: a \: circle = 784 \: \pi}}[/tex]
Using [tex] \sf{\pi \: ≈ \: 3.14}[/tex] , we obtain :
[tex] \longrightarrow{ \sf{Area \: of \: a \: circle = 784 \times 3.14 }}[/tex]
[tex] \longrightarrow{ \boxed{ \sf{Area \: of \: a \: circle = 2461.76 \: {inches}^{2} }}}[/tex]
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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