Answered

Get the most out of your questions with the extensive resources available on IDNLearn.com. Get comprehensive answers to all your questions from our network of experienced experts.

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

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.