Question

a company that manufactures storage bins for grains made a drawing of a silo. the silo has a conical base, as shown below. which of the following could be used to calculate the total volume of grains that can be stored in the silo? π(10ft)²(2ft)+1/3 π(2ft)²(13ft - 10ft) π(2ft)²(10ft)+1/3 π(2ft)²(13ft - 10ft) π(10ft)²(2ft)+1/3 π(13ft - 10ft)²(2ft) π(2ft)²(10ft)+1/3 π(13ft - 10ft)²(2ft)

Explanation:

Step1: Identify the shapes

The silo is composed of a cone and a cylinder.

Step2: Recall volume formulas

Volume of cylinder $V_{cylinder}=\pi r^{2}h$, volume of cone $V_{cone}=\frac{1}{3}\pi r^{2}h$. The radius $r = \frac{4}{2}=2$ ft, height of cylinder $h_{cylinder}=13$ ft, height of cone $h_{cone}=10$ ft.

Step3: Calculate cylinder volume

$V_{cylinder}=\pi(2)^{2}(13)=\pi(4)(13)$

Step4: Calculate cone volume

$V_{cone}=\frac{1}{3}\pi(2)^{2}(10)$

Step5: Calculate total volume

Total volume $V = V_{cone}+V_{cylinder}=\frac{1}{3}\pi(2)^{2}(10)+\pi(2)^{2}(13)$

Answer:

$\frac{1}{3}\pi(2)^{2}(10)+\pi(2)^{2}(13)$