Question
Find the surface area of a sphere with radius, requals=99 in.
Question content area bottom
Part 1
S.A.equals=enter your response here insquared2
Question content area bottom
Part 1
S.A.equals=enter your response here insquared2
Answers
GPT-4o mini
The surface area \( S \) of a sphere can be calculated using the formula:
\[
S = 4\pi r^2
\]
where \( r \) is the radius of the sphere.
Given that the radius \( r = 99 \) inches, we can substitute this value into the formula:
\[
S = 4\pi (99^2)
\]
First, calculate \( 99^2 \):
\[
99^2 = 9801
\]
Now, substitute this back into the surface area formula:
\[
S = 4\pi (9801)
\]
Now calculate \( 4 \times 9801 \):
\[
4 \times 9801 = 39204
\]
Finally, we can express the surface area as:
\[
S = 39204\pi
\]
To get a numerical approximation, use \( \pi \approx 3.14159 \):
\[
S \approx 39204 \times 3.14159 \approx 123,113.12
\]
Therefore, the surface area of the sphere is approximately:
\[
S \approx 123113.12 \, \text{in}^2
\]
So, rounding to two decimal places, the final response is:
\[
S \approx 123113.12 \, \text{in}^2
\]
\[
S = 4\pi r^2
\]
where \( r \) is the radius of the sphere.
Given that the radius \( r = 99 \) inches, we can substitute this value into the formula:
\[
S = 4\pi (99^2)
\]
First, calculate \( 99^2 \):
\[
99^2 = 9801
\]
Now, substitute this back into the surface area formula:
\[
S = 4\pi (9801)
\]
Now calculate \( 4 \times 9801 \):
\[
4 \times 9801 = 39204
\]
Finally, we can express the surface area as:
\[
S = 39204\pi
\]
To get a numerical approximation, use \( \pi \approx 3.14159 \):
\[
S \approx 39204 \times 3.14159 \approx 123,113.12
\]
Therefore, the surface area of the sphere is approximately:
\[
S \approx 123113.12 \, \text{in}^2
\]
So, rounding to two decimal places, the final response is:
\[
S \approx 123113.12 \, \text{in}^2
\]