Question

question 1 (multiple choice worth 2 points) (volume mc)
the propane storage tank shown is a cylinder with a hemisphere on each end.
what is the volume of the propane tank?
602.92 ft³
946.93 ft³
423.33 ft³
513.13 ft³

Explanation:

Step1: Find volume of cylinder

The formula for the volume of a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 7$ feet and $h=11$ feet. So $V_{cylinder}=\pi\times7^{2}\times11=\pi\times49\times11 = 539\pi$ cubic - feet.

Step2: Find volume of two hemispheres

Two hemispheres together form a full - sphere. The formula for the volume of a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. With $r = 7$ feet, $V_{sphere}=\frac{4}{3}\pi\times7^{3}=\frac{4}{3}\pi\times343=\frac{1372\pi}{3}$ cubic - feet.

Step3: Find total volume of the tank

The total volume of the propane tank $V = V_{cylinder}+V_{sphere}$. $V=539\pi+\frac{1372\pi}{3}=\frac{1617\pi + 1372\pi}{3}=\frac{2989\pi}{3}\approx\frac{2989\times3.14}{3}=\frac{9385.46}{3}\approx946.93$ cubic feet.

Answer:

$946.93\ ft^{3}$