Question

A 16 meter long cylinder with a diameter of 7 meters has a square prism with a base length of 2 meters hole going all the way through the center of it as shown in the diagram (not to scale). Find the volume of the composite shape rounding to the nearest cubic meter.

Hint: while working the problem carry figures at least three decimal places, then round to the nearest cubic meter only once at the very end.

Answer 1

mind you that that picture is deceiving, since the 16 meters for its height should be much longer than its 7 meters diameter, but anyhow, let's simply get the volume of the cylinder with a height of 16 meters and a radius of half 7 or namely 3.5 meters, then we'll get the volume of prism which will be 2*2*16 and subtract the volume of the prism from that of the containing cylinder, what's leftover is what we didn't subtract, namely the composite shape.

`\textit{Volume of a Cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3.5\\ h=16 \end{cases}\implies V=\pi (3.5)^2(16)\implies V=784\pi \\\\[-0.35em] ~\dotfill\\\\ \textit{Volume of the Prism}\qquad (2)(2)(16)\implies 64 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Volumes} }{784\pi ~~ - ~~64} ~~ \approx ~~ \text{\LARGE 2399}~m^3`

Answer 2

V = π(7/2)²(16) - 2(2)(16)

= π(49/4)(16) - 64

= 196π - 64

= about 552 cubic meters