Question

A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The cone is tilted at an angle so its peak touches the edge of the cylinder’s base. What is the volume of the space remaining in the cylinder after the cone is placed inside it?

Answer 1

Answer:

Step-by-step explanation:

Given that A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same

Whatever position cone is placed, the space remaining will have volume as

volume of the cylinder - volume of the cone

Let radius of cylinder be r and height be h

Then volume of  cylinder  = $\pi r^2 h$

The cone has height as h and radius as r/2

So volume of cone = $\frac{1}{3} \pi (\frac{r}{2} )^2h\\=(\pi r^2 h)\frac{1}{24}$

the volume of the space remaining in the cylinder after the cone is placed inside it

=$\pi r^2 h (1-\frac{1}{24} )\\=\frac{23 \pi r^2 h}{24}$

Answer 2

Here is the answer: 3/4 (pi r^2 h)