Question

Which is the closest to the volume of the solid that remained?

Answer 1

Check the picture below.

so if we pluck the cylinder from the inside, what's leftover is that cyan ring with a height of 10, well, let's get the area of the ring and simply multiply it by its height.

`\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=15\\ r=11 \end{cases}\implies A=\pi (15^2-11^2)\implies A=104\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{volume of a hollow cylinder}}{104\pi }\cdot 10 ~~ \approx ~~ \text{\LARGE 3267.26}~in^3 ~~ \approx 3266~in^3`