Calculate the volume of a sphere that has a diameter of 7 inches. Use 3.14 for pi and round to the nearest tenth.(1 point)

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1 answer

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

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

where \( V \) is the volume and \( r \) is the radius of the sphere.

First, find the radius. The radius is half of the diameter:

\[ \text{Diameter} = 7 \text{ inches} \ \text{Radius} (r) = \frac{7 \text{ inches}}{2} = 3.5 \text{ inches} \]

Now, substitute the radius into the volume formula. Using \( \pi \approx 3.14 \):

\[ V = \frac{4}{3} \times 3.14 \times (3.5)^3 \]

Calculate \( (3.5)^3 \):

\[ (3.5)^3 = 3.5 \times 3.5 \times 3.5 = 42.875 \]

Now substitute this back into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times 42.875 \]

Calculating \( \frac{4}{3} \times 3.14 \):

\[ \frac{4}{3} \approx 1.3333 \ 1.3333 \times 3.14 \approx 4.1887 \]

Now calculate the volume:

\[ V \approx 4.1887 \times 42.875 \approx 179.594 \]

Finally, round to the nearest tenth:

\[ V \approx 179.6 \text{ cubic inches} \]

The volume of the sphere is approximately 179.6 inches³.