Find the surface area of a sphere with​ radius, requals=99 in.

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Part 1
S.A.equals=enter your response here insquared2

1 answer

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:

\[ S \approx 123113.12 , \text{in}^2 \]