Question

a solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. what is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units

Explanation:

Step1: Calculate volume of cylinder

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$. Given $r = 8$ and $h=15$, we have $V_{cylinder}=\pi\times8^{2}\times15=\pi\times64\times15 = 960\pi$.

Step2: Calculate volume of cone

The volume formula for a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Here $r = 8$ and $h = 15$, so $V_{cone}=\frac{1}{3}\pi\times8^{2}\times15=\frac{1}{3}\pi\times64\times15=320\pi$.

Step3: Calculate unfilled volume

The unfilled volume $V = V_{cylinder}-V_{cone}$. Substitute the values: $V=960\pi - 320\pi=640\pi$.

Answer:

$640\pi$ cubic units