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Question
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
Options
π : 2
π : 3
π : 4
π : 6
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Solution
In the given problem, we are given a sphere inscribed in a cube. So, here we need to find the ratio between the volume of a sphere and volume of a cube. This means that the diameter of the sphere will be equal to the side of the cube. Let us take the diameter as d.
Here,
Volume of a sphere (V1) = `(4/3) pi (d/2)^3`
` = (4/3)pi(d^3/8)`
=`(pi d^3)/6`
Volume of a cube (V2) = S3
`=d^3`
Now, the ratio of the volume of sphere to the volume of the cube = `V_1/V_2`
`V_1/V_2=(((pi d^3)/6))/d^3`
So, the ratio of the volume of sphere to the volume of the cube is π : 6 .
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