Question

a globe company currently manufactures a globe that is 18 inches in diameter. if the dimensions of the globe were reduced by half, what would its volume be? use 3.14 for π and round your answer to the nearest tenth. 3052.1 in³ 121.5 in³ 972.1 in³ 381.5 in³

Explanation:

Step1: Find original radius

The diameter of the original globe is $d = 18$ inches, so the radius $r=\frac{d}{2}=\frac{18}{2}=9$ inches.

Step2: Calculate original volume

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 9$ and $\pi=3.14$ into the formula: $V=\frac{4}{3}\times3.14\times9^{3}=\frac{4}{3}\times3.14\times729 = 4\times3.14\times243=3052.08\approx3052.1$ $in^{3}$.

Step3: Find new - radius

If the dimensions are reduced by half, the new radius $r_{new}=\frac{r}{2}=\frac{9}{2} = 4.5$ inches.

Step4: Calculate new volume

Using the volume formula for a sphere again with $r_{new}=4.5$ inches and $\pi = 3.14$, we have $V_{new}=\frac{4}{3}\times3.14\times4.5^{3}=\frac{4}{3}\times3.14\times91.125=4\times3.14\times30.375 = 381.51\approx381.5$ $in^{3}$.

Answer:

$381.5$ $in^{3}$