Concept explainers
a.
To find: The volume of the largest sphere that can be inscribed in the cube of volume
a.
Answer to Problem 13PSC
The volume of the largest sphere that can be inscribed in the cube is
Explanation of Solution
Given Information:
Volume of a cube
Formula used:
Volume of a cube
Volume of a sphere
Calculation:
Let
We know that, Volume of a cube
As
Now, the largest sphere which fits into a cube will be a sphere of whose diameter is equal to the edge of cube.
Let
Now we know that, Volume of a sphere
Hence, the volume of the largest sphere that can be inscribed in the cube is
b.
To find: The volume of the smallest sphere that can be circumscribed about the cube.
b.
Answer to Problem 13PSC
The volume of the smallest sphere is
Explanation of Solution
Given Information:
Volume of a cube
Formula used:
Volume of a cube
Volume of a sphere
Diagonal of a square
In a right triangle,
Calculation:
Let
We know that, Volume of a cube
As
So, each side of every square base of a cube will be 10 m.
Therefore, diagonal of each surface of a cube will be
Now, the diagonal of a cube
Here,
Using Pythagoras theorem, we have
Now,
Now we know that, Volume of a sphere
Hence, the volume of the smallest sphere that can circumscribe the cube is
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