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MATH / A right circular cone is inscribed in a right circular cylinder. The volume of…

Problem

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problem

A right circular cone is inscribed in a right circular cylinder. The volume of the cylinder is 72π72\pi cubic centimeters. What is the number of cubic centimeters in the space inside the cylinder but outside the cone? Express your answer in terms of π\pi. [asy] import solids; size(150); import three; defaultpen(linewidth(0.8)); currentprojection = orthographic(5,0,3); revolution c = cylinder((0,0,0), 1, 3); revolution c2 = cone((0,0,0), 1, 3); draw(c,black); draw(c2,black); [/asy]
Plain-text mathematical notation (without MathML)
A right circular cone is inscribed in a right circular cylinder. The volume of the cylinder is 72π cubic centimeters. What is the number of cubic centimeters in the space inside the cylinder but outside the cone? Express your answer in terms of π.

[asy]
import solids; size(150); import three; defaultpen(linewidth(0.8)); currentprojection = orthographic(5,0,3);
revolution c = cylinder((0,0,0), 1, 3);
revolution c2 = cone((0,0,0), 1, 3);
draw(c,black);
draw(c2,black);
[/asy]
Original LaTeX notation
A right circular cone is inscribed in a right circular cylinder. The volume of the cylinder is $72\pi$ cubic centimeters. What is the number of cubic centimeters in the space inside the cylinder but outside the cone? Express your answer in terms of $\pi$.

[asy]
import solids; size(150); import three; defaultpen(linewidth(0.8)); currentprojection = orthographic(5,0,3);
revolution c = cylinder((0,0,0), 1, 3);
revolution c2 = cone((0,0,0), 1, 3);
draw(c,black);
draw(c2,black);
[/asy]

level

Level 3

type

Geometry

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Source and history

task_id
1b31efc5-93d9-57fe-a8b1-380ff4ae2a22
task_key
geometry--test--1b31efc5-93d9-57fe-a8b1-380ff4ae2a22
task_revision_id
1
config / split
geometry / test

Official source

initial import