Question

a storage bin has the shape of a cylinder with a conical top. what is the volume of the storage bin if its radius is r = 4.3 ft, the height of the cylindrical portion is h = 7.4 ft, and the overall height is h = 18.2 ft? volume (to the nearest tenth) select an answer

Explanation:

Step1: Find height of cone

The overall height \( H = 18.2 \) ft and cylindrical height \( h = 7.4 \) ft. So cone height \( h_{cone}=H - h=18.2 - 7.4 = 10.8 \) ft.

Step2: Volume of cylinder

Formula for cylinder volume \( V_{cylinder}=\pi r^{2}h \). Substitute \( r = 4.3 \), \( h = 7.4 \):
\( V_{cylinder}=\pi\times(4.3)^{2}\times7.4\approx\pi\times18.49\times7.4\approx423.6 \) (approximate).

Step3: Volume of cone

Formula for cone volume \( V_{cone}=\frac{1}{3}\pi r^{2}h_{cone} \). Substitute \( r = 4.3 \), \( h_{cone}=10.8 \):
\( V_{cone}=\frac{1}{3}\pi\times(4.3)^{2}\times10.8\approx\frac{1}{3}\pi\times18.49\times10.8\approx209.9 \) (approximate).

Step4: Total volume

Add cylinder and cone volumes: \( V = V_{cylinder}+V_{cone}\approx423.6 + 209.9 = 633.5 \) (to nearest tenth).

Answer:

\( 633.5 \) cubic feet