Question

(D) 1-2 ; 2. A cube of wood of side 12cm was cut and formed into a largest sphere. Find out the volume of the sphere?​

Answer 1

Step-by-step explanation:

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Answer 2

The volume of the sphere formed will be 904.32 cm³.

Given,

A wooden cube of side 12 cm,

It is cut and formed into the largest possible sphere.

To find,

The volume of the sphere.

Solution,

It is given here that the side of the cube is 12 cm.

Now, this cube is cut to form the largest sphere.

Let the radius of the sphere formed be $r$. Then, its diameter will be $2r$.

We can see that for the largest sphere to be cut, the diameter of the sphere will be equal to the side of the given cube.

∵ side of the cube = 12 cm

∴ $2r$ = 12 cm

⇒ $r$ = 6 cm.

As the volume of a sphere having radius 'r' is given by,

$V=\frac{4}{3} \pi r^{3}$

Hence, for the given sphere,

$V=\frac{4}{3} \pi (6)^{3}$

$\implies V=\frac{4}{3} \times \pi \times (216)$

$\implies V=4\times (3.14) \times (72)$        [taking $\pi =3.14$]

⇒ V = 904.32 cm³.

Therefore, the volume of the sphere formed will be 904.32 cm³.