To find the surface area and volume of a sphere, we can use the following formulas:
-
Surface Area (A):
\[ A = 4 \pi r^2 \] -
Volume (V):
\[ V = \frac{4}{3} \pi r^3 \]
Where \( r \) is the radius of the sphere.
Given that the diameter of the sphere is 99 inches, the radius \( r \) is half of the diameter:
\[ r = \frac{99}{2} = 49.5 \text{ inches} \]
Now, let's calculate the surface area and volume using \( \pi \approx 3.14 \).
Surface Area: \[ A = 4 \times 3.14 \times (49.5)^2 \]
First, calculate \( (49.5)^2 \): \[ (49.5)^2 = 2450.25 \]
Now, substitute back into the surface area formula: \[ A = 4 \times 3.14 \times 2450.25 \] \[ A \approx 4 \times 3.14 \times 2450.25 \] \[ A \approx 4 \times 7688.78 \] \[ A \approx 30755.12 \text{ square inches} \]
Volume: \[ V = \frac{4}{3} \times 3.14 \times (49.5)^3 \]
First, calculate \( (49.5)^3 \): \[ (49.5)^3 = 12167.875 \]
Now, substitute back into the volume formula: \[ V = \frac{4}{3} \times 3.14 \times 12167.875 \] \[ V \approx 4.18867 \times 12167.875 \] (using \(\frac{4}{3} \times 3.14 \approx 4.18867\)) \[ V \approx 50919.53 \text{ cubic inches} \]
Therefore, the sphere's surface area is approximately 30755.12 square inches, and the volume is approximately 50919.53 cubic inches.
To summarize:
- The sphere's surface area is 30755.12 square inches.
- The sphere's volume is 50919.53 cubic inches.