Question

what is the volume of a sphere with a diameter of 30 units?
14,130 units cubed
12,826 units cubed
11,304 units cubed

Explanation:

Step1: Find the radius

The diameter \( d = 30 \) units, so the radius \( r=\frac{d}{2}=\frac{30}{2} = 15 \) units.

Step2: Use the sphere volume formula

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \). Substitute \( r = 15 \) and \( \pi\approx3.14 \):
\( V=\frac{4}{3}\times3.14\times15^{3} \)
First, calculate \( 15^{3}=15\times15\times15 = 3375 \).
Then, \( \frac{4}{3}\times3.14\times3375=\frac{4\times3.14\times3375}{3} \).
Simplify: \( 4\times3.14\times1125 = 12.56\times1125 = 14130 \)? Wait, no, wait. Wait, maybe I made a mistake. Wait, no, let's recalculate. Wait, \( \frac{4}{3}\times3.14\times15^{3}=\frac{4}{3}\times3.14\times3375 \). \( 3375\div3 = 1125 \), then \( 4\times3.14\times1125 = 12.56\times1125 \). Let's compute \( 12\times1125 = 13500 \), \( 0.56\times1125 = 630 \), so total is \( 13500 + 630 = 14130 \)? But wait, the options have 14130, but wait, maybe the problem uses \( \pi = 3.14 \), but let's check again. Wait, no, maybe I messed up the radius? Wait, diameter is 30, radius 15. Wait, but let's check the options. Wait, the options are 14130, 12826, 11304. Wait, maybe the formula was misapplied? Wait, no, wait, maybe the question is a sphere, but maybe it's a different formula? Wait, no, the volume of a sphere is \( \frac{4}{3}\pi r^{3} \). Wait, let's check with \( \pi = 3.14 \):

\( r = 15 \), so \( r^{3}=3375 \), \( \frac{4}{3}\times3.14\times3375 = 4\times3.14\times1125 = 12.56\times1125 = 14130 \). So the first option is 14,130 units cubed. But wait, maybe the problem has a typo, or maybe I made a mistake. Wait, no, let's check the options again. Wait, the options are 14,130; 12,826; 11,304. Wait, maybe the question is a different shape? No, it's a sphere. Wait, maybe the diameter is 30, but maybe the formula is for a different shape? No, the question says sphere. So according to the calculation, the volume is 14130 cubic units. But wait, let's check the options. The first option is 14,130 units cubed. But wait, maybe I made a mistake in the formula. Wait, no, the volume of a sphere is \( \frac{4}{3}\pi r^{3} \). Let's confirm with another approach. \( \pi\approx3.14 \), \( r = 15 \). So \( V=\frac{4}{3}\times3.14\times3375 = 4\times3.14\times1125 = 12.56\times1125 = 14130 \). So the correct answer should be 14,130 units cubed.

Answer:

14,130 units cubed (the first option)