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?

Volume of cylinder = pi x r^2 x h
Volume of cone = 1/3 x pi x r^2 x h
radius of cone = 1/2 (r)
Remaining volume = Volume of cylinder - Volume of cone
= pi x r^2 x h - 1/3 x pi x (r/2)^2 x h
= pi r^2 h - 1/4 pi r^2 h
= 3/4 (pi r^2 h)

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Lanuel Lanuel · Answer 2 · 2022-05-18T11:34:59+02:00

The volume of the space remaining in the cylinder after the cone is placed inside it is equal to 11/12πr²h.

How to calculate the volume of a cylinder?

Mathematically, the volume of a cylinder is calculated by using this formula:

V = πr²h

Where:

h is the height.

r is the radius.

For the cone, we have:

Volume of cone = 1/3πr²h

Also, the radius of cone is equal to half the radius of the cylinder:

r = r/2

Therefore, the volume of the space remaining in the cylinder after the cone is placed inside it, is given by:

Remaining volume = Volume of cylinder - Volume of cone

Remaining volume = πr²h - 1/3 π(r/2)²h

Remaining volume = πh(r² - 1/3 × r²/4)

Remaining volume = πh(r² - r²/12)

Remaining volume = πh(11r²/12)

Remaining volume = 11/12πr²h.

Read more on cylinder here: brainly.com/question/21367171

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