Question

a cylinder has been drilled out of this block to allow a rod to pass through. all measurements are in millimeters. lets find the remaining volume of the block.

Explanation:

Step1: Calculate volume of the block

The block is a rectangular - prism. The volume formula for a rectangular - prism is $V_{block}=l\times w\times h$. Here, $l = 7$, $w = 11$, and $h = 9$. So $V_{block}=7\times11\times9=693$ $mm^{3}$.

Step2: Calculate volume of the cylinder

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$. The radius $r = 3$ and the height (length of the block) $h = 11$. So $V_{cylinder}=\pi\times3^{2}\times11=\pi\times9\times11 = 99\pi\approx99\times3.14 = 310.86$ $mm^{3}$.

Step3: Calculate the remaining volume

The remaining volume $V = V_{block}-V_{cylinder}$. So $V=693 - 310.86=382.14$ $mm^{3}$.

Answer:

$382.14$ $mm^{3}$