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High School
Geometry
High school geometry
Finding volume

Charlee Sweeney

Answered question

2022-12-23

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.

Answer & Explanation

bagosiwp2

Beginner2022-12-24Added 16 answers

We have: The edge of cube = 9 cm

\Rightarrow

This will be the altitude of the cone.
So,
The radius of circular cone will be 9/2 = 4.5 cm.
As we are aware,
The volume of cone is given by formula:

V = \frac{1}{3} π R^{2} H

where,
R is the radius and H the altitude of cone.
Additionally, the largest cone that we can find must have a volume that is equal to or lower than that of a cube.

V = \frac{1}{3} π R^{2} H

= \frac{1}{3} π (4.5)^{2} \times 9

= \frac{1}{3} π 20.25 \times 9

= \frac{1}{3} \times \frac{22}{7} \times 20.25 \times 9 = 190.92 c m^{3}

Required volume is

190.92 c m^{3}

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