Question

Find the area of the circle.
12 ft

Answer 1

`\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}`

Answer 2

• 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