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If a circle has a diameter of 16 feet, which expression gives its area in square feet?

A. [tex]\(16 \cdot \pi\)[/tex]
B. [tex]\(8 \cdot \pi\)[/tex]
C. [tex]\(16^2 \cdot \pi\)[/tex]
D. [tex]\(8^2 \cdot \pi\)[/tex]

Sagot :

GinnyAnsweridn
To determine the area of a circle, we use the formula:

[tex]\[ \text{Area} = \pi r^2 \][/tex]

where [tex]\( r \)[/tex] is the radius of the circle.

Given that the diameter of the circle is 16 feet, we first need to find the radius. The radius is half of the diameter:

[tex]\[ r = \frac{\text{diameter}}{2} \][/tex]

So for a diameter of 16 feet:

[tex]\[ r = \frac{16}{2} = 8 \text{ feet} \][/tex]

Next, we substitute the radius into the area formula to get:

[tex]\[ \text{Area} = \pi \times (8)^2 \][/tex]

Calculating [tex]\( 8^2 \)[/tex]:

[tex]\[ 8^2 = 64 \][/tex]

Therefore, the area of the circle is:

[tex]\[ \text{Area} = 64 \pi \text{ square feet} \][/tex]

Among the given expressions:
A. [tex]\( 16 \cdot \pi \)[/tex]
B. [tex]\( 8 \cdot \pi \)[/tex]
C. [tex]\( 16^2 \cdot \pi \)[/tex]
D. [tex]\( 8^2 \cdot \pi \)[/tex]

The correct expression that represents the area in square feet is:

[tex]\[ \boxed{8^2 \cdot \pi} \][/tex]

Thus, the answer is option D.
Wegnerkolmp2741oidn

Answer:

D. 8^2 π

Step-by-step explanation:

To find the area of a circle, we use the formula

A = pi r^2 where r is the radius

We are given the diameter, which is twice the radius.

d = 2r

16 = 2r

8 =r

The radius is 8

A = pi * 8^2

A = 64 pi

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