Question
Surface Area of Spheres Practice
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Question
Find the surface area of a sphere with a diameter of 40 inches. Leave your answer in terms of pi.(1 point)
The surface area is
in.2
Answers
GPT-4o mini
To find the surface area of a sphere, you can use the formula:
\[
\text{Surface Area} = 4\pi r^2
\]
where \( r \) is the radius of the sphere.
First, find the radius from the diameter. The diameter given is 40 inches, so the radius \( r \) is:
\[
r = \frac{\text{Diameter}}{2} = \frac{40 \text{ inches}}{2} = 20 \text{ inches}
\]
Now, plug the radius into the surface area formula:
\[
\text{Surface Area} = 4\pi (20)^2
\]
Calculating \( (20)^2 \):
\[
(20)^2 = 400
\]
Now substitute back into the equation:
\[
\text{Surface Area} = 4\pi \times 400
\]
\[
\text{Surface Area} = 1600\pi
\]
Thus, the surface area of the sphere is:
\[
\text{Surface Area} = 1600\pi \text{ in}^2
\]
So, the surface area is \( 1600\pi \) in².
\[
\text{Surface Area} = 4\pi r^2
\]
where \( r \) is the radius of the sphere.
First, find the radius from the diameter. The diameter given is 40 inches, so the radius \( r \) is:
\[
r = \frac{\text{Diameter}}{2} = \frac{40 \text{ inches}}{2} = 20 \text{ inches}
\]
Now, plug the radius into the surface area formula:
\[
\text{Surface Area} = 4\pi (20)^2
\]
Calculating \( (20)^2 \):
\[
(20)^2 = 400
\]
Now substitute back into the equation:
\[
\text{Surface Area} = 4\pi \times 400
\]
\[
\text{Surface Area} = 1600\pi
\]
Thus, the surface area of the sphere is:
\[
\text{Surface Area} = 1600\pi \text{ in}^2
\]
So, the surface area is \( 1600\pi \) in².