Question

Find the surface area and volume for the sphere below. Use 3.14 for π. Click Here for Help Video





99
99 inches


The sphere's surface area is
square inches.



The sphere's volume is
cubic inches.

Answer 1

To find the surface area and volume of a sphere, we can use the following formulas:

1. **Surface Area (A)**:
\[ A = 4 \pi r^2 \]

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**.