Question

The diameter of a sphere is 2 ft. What is the sphere's volume? Round to the nearest tenth.
Responses
A 4.2
4.2 ft^3
B 8.1
8.1 ft^3
C 16.8
16.8 ft^3
D 33.5 ft^3

Answer 1

To calculate the volume of a sphere, you can use the formula:

\[
V = \frac{4}{3} \pi r^3
\]

where \( r \) is the radius of the sphere.

Given that the diameter of the sphere is 2 ft, the radius \( r \) can be calculated as:

\[
r = \frac{\text{diameter}}{2} = \frac{2 \text{ ft}}{2} = 1 \text{ ft}
\]

Now, plug the radius into the volume formula:

\[
V = \frac{4}{3} \pi (1 \text{ ft})^3
\]

Calculating \( (1 \text{ ft})^3 \):

\[
(1 \text{ ft})^3 = 1 \text{ ft}^3
\]

So now we have:

\[
V = \frac{4}{3} \pi (1 \text{ ft}^3) = \frac{4}{3} \pi \text{ ft}^3
\]

Using \( \pi \approx 3.14159 \):

\[
V \approx \frac{4}{3} \times 3.14159 \approx 4.18879 \text{ ft}^3
\]

Rounding this to the nearest tenth:

\[
V \approx 4.2 \text{ ft}^3
\]

The correct answer is therefore:

**A. 4.2 ft³**