Question

which of the following could be used to calculate the total volume of grains that can be stored in the silo?
π(2ft)²(8ft) + 1/3π(2ft)²(9.5ft - 8ft)
π(8ft)²(2ft) + 1/3π(2ft)²(9.5ft - 8ft)
π(2ft)²(8ft) + 1/3π(9.5ft - 8ft)²(2ft)
π(8ft)²(2ft) + 1/3π(9.5ft - 8ft)²(2ft)

Explanation:

Step1: Identify the shapes

The silo is composed of a cylinder and a cone. The cylinder has height $h_{cylinder}=8$ ft and radius $r = 2$ ft. The cone has height $h_{cone}=9.5 - 8=1.5$ ft and radius $r = 2$ ft.

Step2: Recall volume formulas

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$ and for a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$.

Step3: Calculate total volume

Substitute the values of $r$, $h_{cylinder}$ and $h_{cone}$ into the formulas. The total volume $V = V_{cylinder}+V_{cone}=\pi(2\text{ft})^{2}(8\text{ft})+\frac{1}{3}\pi(2\text{ft})^{2}(9.5\text{ft}-8\text{ft})$.

Answer:

$\pi(2\text{ft})^{2}(8\text{ft})+\frac{1}{3}\pi(2\text{ft})^{2}(9.5\text{ft}-8\text{ft})$