Question

nabhitha measure the volume of a sink basin by modeling it as a hemisphere. nabhitha measures its radius to be $15\frac{1}{4}$ inches. find the sink’s volume in cubic inches. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Convert mixed - number to improper fraction

$15\frac{1}{4}=\frac{15\times4 + 1}{4}=\frac{61}{4}$ inches.

Step2: Recall the volume formula for a hemisphere

The volume formula for a hemisphere is $V=\frac{2}{3}\pi r^{3}$.

Step3: Substitute the radius into the formula

$V=\frac{2}{3}\pi(\frac{61}{4})^{3}=\frac{2}{3}\pi\times\frac{61^{3}}{4^{3}}=\frac{2}{3}\pi\times\frac{226981}{64}=\frac{226981\pi}{96}$.

Step4: Calculate the value

$V=\frac{226981\pi}{96}\approx\frac{226981\times3.14159}{96}\approx\frac{713057.77779}{96}\approx7427.7$.

Answer:

$7427.7$ cubic inches.