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Sagot :
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.
[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.
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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