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Find the area of the circle.
12 ft

Find the area of the circle. 12 ft-example-1

2 Answers

11 votes


\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{70}{1}

Find the area of the circle (diameter = 12 ft)


\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}

We're asked to find the area of the circle, which can be found using the

following formula:-


\longmapsto\underline{\boxed{\bold{A=\pi r^2}}}

Where:-

  • A=area
  • π=pi (3.14...)
  • r=radius

Provided Information:-

  • diameter (d) = 12 ft

What to do:-


\bigstar Notice that we have the diameter and not the radius.


\bigstar Since the radius is exactly one-half of the diameter, we divide the

diameter by 2 and get the radius:-


\longmapsto\sf{d=2r}


\bigstar Rearranging the formula,


\longmapsto\large\text{$r=\displaystyle(d)/(2)$}


\bigstar Substituting the required value (d=12) in lieu of d:-


\longmapsto\large\text{r=$\displaystyle(12)/(2)$}


\bigstar Circle's Radius:-


\longmapsto\large\text{\boxed{\boxed{r=6}}}


\triangle\rule{300}{1}\triangle

Now that we have the radius, let's find the area.

Remember, we need the following formula:-


\longmapsto\underline{\boxed{\sf{A=\pi r^2}}}


\bigstar Substituting the required value (r=6) into the formula,


\longmapsto\underline{\boxed{\sf{A=\pi (6)^2}}}


\bigstar Squaring the radius,


\longmapsto\underline{\boxed{\sf{A=\pi *36}}}


\bigstar Now, Substitute 3.14 for pi:-


\longmapsto\sf{A=3.14*36}


\bigstar Multiplying the values,


\longmapsto\sf{A=113.04\:ft^2}

  • Henceforth, We conclude that the right option is:-


\longmapsto\Large\underline{\boxed{\text{Option\:D}}}

Good luck with your studies.

#TogetherWeGoFar


\rule{300}{1}

User Kingamajick
by
8.9k points
13 votes

Answer:

  • Area of the circle is 113.04 ft²

Explanation:

Given:

  • Diameter of circle = 12 feet

To Find:

  • Area of the circle

Using formula:


\\ \: \: \dashrightarrow \: \: \:{\underline{\boxed{ \bf{Area_(( circle)) = \pi r^2}}}} \\ \\

Where,

  • π = 3.14
  • Diameter = 12 feet
  • Radius = 12/2 = 6 feet

On substituting the required values, we get:


\\ \: \: \dashrightarrow \: \: \: \sf Area_((Circle)) = 3.14 * {(6)}^(2) \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf Area_((Circle)) = 3.14 * 36 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf Area_((Circle)) = 113.04 \: {ft}^(2) \\ \\ \\

Hence,

  • Area of the circle is 113.04 ft²
User Kevin Andrid
by
7.7k points

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