Question

I need a well explained solution plss..

Answer 1

In order to solve this Problem, We need to Notice One thing, That is :

When the Piece of Metal in the Shape of Cone is Changed to Shape of Cube, there is no change in the Volume, that is the Volume of Cone should be Equal to Volume of Cube, Because no matter is lost during the Process of Changing of Shape from Cone to Cube. So, Volume remains Constant.

Let us First Find the Volume of Cone :

We know that Volume of Cone is Given by : $\frac{\pi r^2h}{3}$

Given : Radius of cone = 3 cm

            Height of the cone = 7 cm

Substituting the above Values in Volume of Cone Formula we get :

Volume of Cone = $\frac{1}{3}\times\frac{22}{7}\times3\times3\times7 = 66\;cm^3$

Now we noticed that Volume of Cone should be Equal to Volume of Cube formed.

⇒ Volume of Cube = 66 cm³

We know that Volume of Cube = S³

where 'S' is the side of the Cube

⇒ S³ = 66

⇒ $S = \sqrt[3]{66} = 4.04\;cm$

⇒ Side of the Cube is 4 cm (Approx)