Answer :
To find the surface area of a sphere with a given circumference, we can follow these steps:
1. First, we must know the formulas:
- The formula for the circumference (C) of a sphere is related to the radius (r) as follows:
\[ C = 2 \pi r \]
- The surface area (SA) of a sphere is given by the formula:
\[ SA = 4 \pi r^2 \]
2. Given that the circumference (C) is 27 inches, we can use it to find the radius (r). Rearranging the circumference formula to solve for r gives:
\[ r = \frac{C}{2 \pi} \]
3. Substitute the value of C (27 inches) into the formula to get the radius:
\[ r = \frac{27}{2 \pi} \]
This will give us the exact radius in inches.
4. Now we have the radius, and we need to use the surface area formula to find the surface area. We substitute our expression for r into the surface area formula:
\[ SA = 4 \pi \left( \frac{27}{2 \pi} \right)^2 \]
5. Simplifying this expression, the surface area (SA) is calculated.
6. Finally, we round the surface area to the nearest whole number as per the instructions.
Following these steps, we find that the surface area of a sphere with a circumference of 27 inches, when rounded to the nearest whole number, is 232 square inches.
