Question

question 1 (multiple choice worth 4 points)
(06.02 lc)
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(2π)²(8π) + 1/3 π(2π)²(9.5π - 8π)
○ π(8π)²(2π) + 1/3 π(2π)²(9.5π - 8π)
○ π(2π)²(8π) + 1/3 π(8π)²(9.5π - 8π)
○ π(8π)²(2π) + 1/3 π(9.5π - 8π)²(2π)

Explanation:

Step1: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V_{cylinder}=\pi r^{2}h\). The diameter \(d = 4\) ft, so the radius \(r=\frac{d}{2}=2\) ft. The height of the cylinder \(h = 8\) ft. Then \(V_{cylinder}=\pi(2)^{2}\times8\).

Step2: Calculate the volume of the cone

The formula for the volume of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). The radius \(r = 2\) ft. The height of the cone \(h=9.5 - 8=1.5\) ft. Then \(V_{cone}=\frac{1}{3}\pi(2)^{2}\times1.5\).

Step3: Calculate the total volume

The total volume \(V = V_{cylinder}+V_{cone}=\pi(2)^{2}(8)+\frac{1}{3}\pi(2)^{2}(1.5)\)

Answer:

\(\pi(2n)^{2}(8n)+\frac{1}{3}\pi(2n)^{2}(9.5n - 8n)\) (where \(n = 1\) in the context of the problem's units, and this matches the form of the fourth option \(\pi(2n)^{2}(8n)+\frac{1}{3}\pi(2n)^{2}(9.5n - 8n)\))