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Dafna11 [192]
2 years ago
13

Find the area of the circle. 12 ft

Mathematics
2 answers:
Ratling [72]2 years ago
3 0

Answer:

  • Area of the circle is 113.04 ft²

Step-by-step explanation:

Given:

  • Diameter of circle = 12 feet

To Find:

  • Area of the circle

Using formula:

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

<em>Where,</em>

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

On substituting the required values, we get:

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

Hence,

  • Area of the circle is<u> </u>113.04 ft²
alexgriva [62]2 years ago
3 0

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

           <em>Find the area of the circle (diameter = 12 ft)</em>

<em>        </em>\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{$r=\displaystyle\frac{d}{2}$}

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

\longmapsto\large\text{r=$\displaystyle\frac{12}{2}$}

\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 \times36}}}

\bigstar Now, Substitute 3.14 for pi:-

\longmapsto\sf{A=3.14\times36}

\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}}}

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

\rule{300}{1}

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