Question

1. a candy package is in the shape of a cylinder with a cone on each end.

if the radius of the cylinder is 2 inches and the cones are identical, what is the capacity of the container to the nearest cubic inch?
a. 33
b. 100
c. 134
d. 201

Explanation:

Step1: Calculate the height of the cone

The total length is \(16\) inches and the length of the cylinder is \(8\) inches. Since there are two identical cones, the combined height of the two cones is \(16 - 8=8\) inches. So the height of one cone \(h = 4\) inches.

Step2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V_{cylinder}=\pi r^{2}h_{cylinder}\). Given \(r = 2\) inches and \(h_{cylinder}=8\) inches. Then \(V_{cylinder}=\pi\times(2)^{2}\times8=\pi\times4\times8 = 32\pi\)

Step3: Calculate the volume of the two cones

The formula for the volume of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). Since there are two cones, \(V_{two - cones}=2\times\frac{1}{3}\pi r^{2}h\). Substituting \(r = 2\) inches and \(h = 4\) inches, we get \(V_{two - cones}=2\times\frac{1}{3}\pi\times(2)^{2}\times4=\frac{32}{3}\pi\)

Step4: Calculate the total volume

\(V = V_{cylinder}+V_{two - cones}\). \(V=32\pi+\frac{32}{3}\pi=\frac{96\pi + 32\pi}{3}=\frac{128\pi}{3}\). Using \(\pi\approx3.14\), \(V=\frac{128\times3.14}{3}=\frac{401.92}{3}\approx134\)

Answer:

C. 134