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

MCQ

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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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 21 Surface Areas and Volume of a Sphere
Q 5 | Page 25