What is the volume of a sphere with a diameter of 27.3 in, rounded to the nearest tenth of a cubic inch?

To find 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 27.3 inches, the radius \( r \) is half of the diameter:

\[
r = \frac{27.3}{2} = 13.65 \text{ inches}
\]

Now, substitute the radius into the volume formula:

\[
V = \frac{4}{3} \pi (13.65)^3
\]

Calculating this:

\[
V \approx \frac{4}{3} \times 3.1416 \times 2542.022
\]

\[
V \approx 10664.205 \text{ cubic inches}
\]

Rounding to the nearest tenth:

\[
V \approx 10664.2 \text{ cubic inches}
\]

So, the volume of the sphere is approximately **10,664.2 cubic inches**.

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How does the volume change if the diameter is doubled?
2. What is the surface area of the same sphere?
3. How do you derive the formula for the volume of a sphere?
4. What is the volume of a hemisphere with the same radius?
5. How does the volume of a sphere compare to the volume of a cylinder with the same height and diameter?

**Tip:** Remember that the volume of a sphere grows rapidly as the radius increases, since it’s proportional to the cube of the radius.

Learn how to calculate the volume of a sphere with a diameter of 27.3 inches using the volume formula. This problem explores geometric concepts related to spheres and includes a step-by-step calculation rounded to the nearest tenth of a cubic inch.

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