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Question
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
Options
27 \[\pi\] cm3
36 \[\pi\] cm3
108 \[\pi\] cm3
12 \[\pi\] cm3
Solution
In the given problem, the largest sphere is carved out of a cube and we have to find the volume of the sphere.
Side of a cube = 6 cm
So, for the largest sphere in a cube, the diameter of the sphere will be equal to side of the cube.
Therefore, diameter of the sphere = 6 cm
Radius of the sphere = 3 cm
Now, the volume of the sphere = `(4/3)pi r^3`
`=(4/3) pi (3)^3 `
= 36 π
Therefore, the volume of the largest sphere inside the given cube is 36 π .
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