Question

find the volume of this object. use 3 for $pi$. volume of a cylinder v = $pi r^{2}h$

Explanation:

Step1: Find radius of upper - cylinder

The diameter of the upper - cylinder is 6 in, so the radius $r_1=\frac{6}{2}=3$ in.

Step2: Calculate volume of upper - cylinder

Using the formula $V = \pi r^{2}h$, with $\pi = 3$, $r_1 = 3$ in and $h_1=8$ in. So $V_1=3\times3^{2}\times8=3\times9\times8 = 216$ in³.

Step3: Find radius of lower - cylinder

The diameter of the lower - cylinder is 10 in, so the radius $r_2=\frac{10}{2}=5$ in.

Step4: Calculate volume of lower - cylinder

Using the formula $V=\pi r^{2}h$, with $\pi = 3$, $r_2 = 5$ in and $h_2 = 2$ in. So $V_2=3\times5^{2}\times2=3\times25\times2=150$ in³.

Step5: Calculate total volume

The total volume $V = V_1+V_2$. So $V=216 + 150=366$ in³.

Answer:

366 in³