Question

what is the surface area of this sphere? round your answer to the nearest hundredth. sphere image with radius 65 in square inches submit

Explanation:

Step1: Recall the formula for the surface area of a sphere

The formula for the surface area \( S \) of a sphere with radius \( r \) is \( S = 4\pi r^{2} \).

Step2: Identify the radius of the sphere

From the diagram, the radius \( r = 65 \) inches.

Step3: Substitute the radius into the formula

Substitute \( r = 65 \) into the formula: \( S = 4\pi(65)^{2} \).

First, calculate \( 65^{2} = 4225 \).

Then, multiply by 4: \( 4\times4225 = 16900 \).

So, \( S = 16900\pi \).

Step4: Calculate the numerical value

Using \( \pi \approx 3.1415926535 \), we have \( S \approx 16900\times3.1415926535 \).

\( 16900\times3.1415926535 = 16900\times3 + 16900\times0.1415926535 = 50700 + 16900\times0.1415926535 \)

\( 16900\times0.1415926535 \approx 16900\times0.1416 = 16900\times0.1 + 16900\times0.04 + 16900\times0.0016 = 1690 + 676 + 27.04 = 2393.04 \)

Then, \( 50700 + 2393.04 = 53093.04 \) (approximate, but more accurately, \( 16900\times3.1415926535 \approx 53092.9158457 \))

Step5: Round to the nearest hundredth

The number \( 53092.9158457 \) rounded to the nearest hundredth is \( 53092.92 \) (since the thousandth digit is 5, we round up the hundredth digit).

Answer:

\( 53092.92 \)