Question

What is the formula to calculate the surface area and volume of a sphere with a radius of 8 yards, using 3.14 for π?

Answer 1

To calculate the surface area and volume of a sphere, you 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 the radius \( r = 8 \) yards and using \( \pi \approx 3.14 \):

**Calculating the surface area:**
\[
A = 4 \times 3.14 \times (8)^2
\]
\[
A = 4 \times 3.14 \times 64
\]
\[
A = 4 \times 3.14 \times 64 = 4 \times 200.96 = 803.84 \text{ square yards}
\]

**Calculating the volume:**
\[
V = \frac{4}{3} \times 3.14 \times (8)^3
\]
\[
V = \frac{4}{3} \times 3.14 \times 512
\]
\[
V = \frac{4 \times 3.14 \times 512}{3} = \frac{6428.48}{3} = 2142.82667 \text{ cubic yards} \approx 2142.83 \text{ cubic yards}
\]

Thus, the surface area of the sphere is approximately **803.84 square yards**, and the volume is approximately **2142.83 cubic yards**.