Question

Find the volume of the largest sphere that can be carved out of a cube of side 21 cm.​

Answer 1

Answer:

Step-by-step explanation:

the greatest sphere that can be cut from the cube of side 21cm, means the diameter of the sphere will be 21cm.

therefore radius of the sphere=21/2cm  

volume of the sphere=4/3πr³  

=4/3×22/7×21/2×21/2×21/2

=11×21×21  

=4851cm³

hence volume of the sphere is 4851cm³.

given side of the cube=21cm  

volume of the cube=side³

=21³

=9261cm³

volume of the remaining portion of the cube if the sphere has been cut from the cube=9261-4851

                      =4410cm³

Answer 2

Concept:

A sphere is a three-dimensional equivalent of a two-dimensional circle. A sphere is a collection of points in three-dimensional space that are all the same distance r from a given point. The supplied point is the sphere's centre, and r is the radius of the sphere.

Find:

The volume of the largest sphere that can be carved from the sphere.

Solution:

The diameter of the largest sphere must be equal to the side of the cube.

$d=21cm\\\\r=\frac{d}{2} \\\\r=\frac{21}{2}$

The volume of the largest sphere is

$V=\frac{4}{3}*\pi*r^3\\\\ V=\frac{4}{3}*\pi*(\frac{21}{2})^3\\\\ V=4851cm^3$

Hence, the volume of the largest sphere is $4851cm^3$.

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