Question

Find the surface area and volume of a sphere that has a diameter of
50
50 inches. Use 3.14 for π. Click Here for Help Video



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) of a sphere:
\[
A = 4\pi r^2
\]
2. Volume (V) of a sphere:
\[
V = \frac{4}{3}\pi r^3
\]

Given that the diameter of the sphere is 50 inches, we can find the radius by dividing the diameter by 2:
\[
r = \frac{50}{2} = 25 \text{ inches}
\]

### Surface Area Calculation

Using the surface area formula:
\[
A = 4\pi r^2
\]
Substituting \(r = 25\) inches and \(\pi = 3.14\):
\[
A = 4 \times 3.14 \times (25)^2
\]
Calculating \((25)^2\):
\[
25^2 = 625
\]
Now substituting back:
\[
A = 4 \times 3.14 \times 625
\]
Calculating \(4 \times 3.14\):
\[
4 \times 3.14 = 12.56
\]
Now,
\[
A = 12.56 \times 625
\]
Finally, calculating \(12.56 \times 625\):
\[
A = 7850 \text{ square inches}
\]

### Volume Calculation

Using the volume formula:
\[
V = \frac{4}{3}\pi r^3
\]
Substituting \(r = 25\) inches and \(\pi = 3.14\):
\[
V = \frac{4}{3} \times 3.14 \times (25)^3
\]
Calculating \((25)^3\):
\[
25^3 = 15625
\]
Now substituting back:
\[
V = \frac{4}{3} \times 3.14 \times 15625
\]
Calculating \(\frac{4}{3} \times 3.14\):
\[
\frac{4 \times 3.14}{3} = \frac{12.56}{3} \approx 4.1867
\]
Now,
\[
V = 4.1867 \times 15625
\]
Calculating \(4.1867 \times 15625\):
\[
V \approx 65261.25 \text{ cubic inches}
\]

### Final Results

- The sphere's surface area is approximately **7850 square inches**.
- The sphere's volume is approximately **65261.25 cubic inches**.