Question

1. medium

this half cylinder fish tank has a tank height of 25 inches and
a tank diameter of 22 inches. what is the volume of this fish
tank?

• please answer all required questions

remaining 1 of 8

Explanation:

Step1: Find the radius of the cylinder

The diameter \(d = 22\) inches. The radius \(r=\frac{d}{2}=\frac{22}{2}=11\) inches.

Step2: Recall the volume formula for a full - cylinder and then adjust for a half - cylinder

The volume formula for a full cylinder is \(V=\pi r^{2}h\). For a half - cylinder, the volume formula is \(V=\frac{1}{2}\pi r^{2}h\).
Substitute \(r = 11\) inches and \(h = 25\) inches into the formula:
\(V=\frac{1}{2}\times\pi\times(11)^{2}\times25\)
First, calculate \((11)^{2}=121\).
Then, \(V=\frac{1}{2}\times\pi\times121\times25=\frac{121\times25}{2}\pi\)
\(121\times25 = 3025\), so \(V=\frac{3025}{2}\pi\)
Take \(\pi\approx3.14\), then \(V=\frac{3025}{2}\times3.14\)
\(\frac{3025}{2}=1512.5\)
\(V = 1512.5\times3.14=4749.25\) cubic inches

Answer:

\(4749.25\) cubic inches