Question

find the volume of this object. use 3 for π. volume of a cylinder v = πr²h volume of a sphere v = $\frac{4}{3}$πr³

Explanation:

Step1: Calculate volume of the sphere

The radius of the sphere $r = 2$ in. Using the formula $V_{sphere}=\frac{4}{3}\pi r^{3}$ and substituting $\pi = 3$ and $r = 2$:
$V_{sphere}=\frac{4}{3}\times3\times2^{3}=\frac{4}{3}\times3\times8 = 32$ in³

Step2: Calculate volume of the cylinder

The radius of the cylinder $r=\frac{4}{2}=2$ in and height $h = 3$ in. Using the formula $V_{cylinder}=\pi r^{2}h$ and substituting $\pi = 3$, $r = 2$ and $h=3$:
$V_{cylinder}=3\times2^{2}\times3=3\times4\times3 = 36$ in³

Step3: Calculate total volume

The total volume $V = V_{sphere}+V_{cylinder}$.
$V=32 + 36=68$ in³

Answer:

68 in³