Question

find the volume of this object. use 3 for π. volume of a cone v = \frac{πr^{2}h}{3} volume of a rectangular prism v = lwh

Explanation:

Step1: Calculate radius of cone

Radius $r$ is half of diameter. Given diameter of cone is $6$ in, so $r=\frac{6}{2}=3$ in.

Step2: Calculate volume of cone

Use formula $V_{cone}=\frac{\pi r^{2}h}{3}$. Substitute $\pi = 3$, $r = 3$ in and $h = 8$ in.
$V_{cone}=\frac{3\times3^{2}\times8}{3}=3\times9\times\frac{8}{3}=72$ $in^{3}$.

Step3: Calculate volume of rectangular - prism

Use formula $V_{prism}=lwh$. Substitute $l = 9$ in, $w = 9$ in and $h = 1$ in.
$V_{prism}=9\times9\times1 = 81$ $in^{3}$.

Step4: Calculate total volume

Total volume $V=V_{cone}+V_{prism}$.
$V=72 + 81=153$ $in^{3}$.

Answer:

$153$