Question

find the volume of this object. use 3 for π. volume of a cylinder v = πr²h volume of a cone v = \frac{πr²h}{3} first let’s calculate the volume of the cylinder. v = π4²12 v ≈ (3)(?)(12) hint: following order of operations, first calculate the value of 4², or 4·4.

Explanation:

Step1: Calculate cylinder volume

The radius of the cylinder $r = \frac{8}{2}=4$ cm and height $h = 12$ cm. Using the formula $V_{cylinder}=\pi r^{2}h$ with $\pi = 3$, we first calculate $r^{2}=4^{2}=16$. Then $V_{cylinder}=3\times16\times12 = 576$ $cm^{3}$.

Step2: Calculate cone volume

The radius of the cone $r = 4$ cm and height $h = 10$ cm. Using the formula $V_{cone}=\frac{\pi r^{2}h}{3}$ with $\pi = 3$, we have $V_{cone}=\frac{3\times4^{2}\times10}{3}$. First, $4^{2}=16$, then $V_{cone}=3\times16\times\frac{10}{3}=160$ $cm^{3}$.

Step3: Calculate total volume

The total volume of the object $V = V_{cylinder}+V_{cone}=576 + 160=736$ $cm^{3}$.

Answer:

$736$ $cm^{3}$