MCQ

The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be

#### Options

27 \[\pi\] cm

^{3}36 \[\pi\] cm

^{3}108 \[\pi\] cm

^{3}12 \[\pi\] cm

^{3}

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#### 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 ****.**

Concept: Surface Area of a Sphere

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