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

inches?

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, we need to find the radius. The radius is half of the diameter, so:

\[ r = \frac{diameter}{2} = \frac{7 \text{ inches}}{2} = 3.5 \text{ inches} \]

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

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

First, calculate \( (3.5)^3 \):

\[ (3.5)^3 = 3.5 \times 3.5 \times 3.5 = 12.25 \times 3.5 = 42.875 \]

Now, substitute \( 42.875 \) back into the volume formula:

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

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

\[ \frac{4}{3} \times 3.14 \approx 4.1867 \]

Now multiply that by \( 42.875 \):

\[ V \approx 4.1867 \times 42.875 \approx 179.1904 \]

Finally, rounding to the nearest tenth gives:

\[ V \approx 179.2 \text{ cubic inches} \]

So the volume of the sphere is approximately 179.2 cubic inches.