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The area of a circle is [tex]$36 \pi$[/tex]. What is the length of the diameter of the circle?

A. 12
B. [tex]$6 \sqrt{2}$[/tex]
C. [tex][tex]$\frac{\pi}{2}$[/tex][/tex]
D. [tex]$\frac{8}{\pi}$[/tex]



Answer :

GinnyAnswer
To determine the length of the diameter of the circle, we need to start with the area of the circle and use the relationship between the area, radius, and diameter.

Step 1: Recall the formula for the area of a circle
The formula for the area of a circle is given by:
[tex]\[ \text{Area} = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.

Step 2: Use the given area to find the radius
The area of the circle is given as [tex]\( 36 \pi \)[/tex]. Using the formula:
[tex]\[ 36 \pi = \pi r^2 \][/tex]

Step 3: Solve for [tex]\( r^2 \)[/tex]
Divide both sides of the equation by [tex]\( \pi \)[/tex]:
[tex]\[ 36 = r^2 \][/tex]

Step 4: Solve for [tex]\( r \)[/tex]
Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{36} \][/tex]
[tex]\[ r = 6 \][/tex]

Step 5: Determine the diameter
The diameter of a circle is twice the radius:
[tex]\[ \text{Diameter} = 2r \][/tex]
[tex]\[ \text{Diameter} = 2 \times 6 \][/tex]
[tex]\[ \text{Diameter} = 12 \][/tex]

Therefore, the length of the diameter of the circle is [tex]\( 12 \)[/tex].

The correct answer is:
A. 12
wegnerkolmp2741o

Answer:

A. 12

Step-by-step explanation:

The formula for area of a circle is

A = pi r^2

36 pi = pi r^2

Divide each side by pi

36 = r^2

Taking the square root of each side:

6 = r

The radius is 6.

To find the diameter, multiply each side by 2.

2r = d

2*6 = d

12 = d

The diameter is 12.

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