Question

A largest possible sphere had been carved from a cubical wooden block of edge 42 cm. find the volume of the carved out wood​

Answer 1

Volume of the carved out wood​ is 35280 cm³

Step-by-step explanation:

• Given data

        Size of side of cube (a)= 42 cm

        Maximum diameter of sphere made from cube (D) = 42 cm

        So

        Maximum radius of sphere made from cube (D) = 21 cm

        $\mathbf{value\ of\ (\pi )=\frac{22}{7}}$

• We know the formula of volume of cube = Side³

        Means

        Volume of cube = Side³ =42³ = 74088 cm³      ...1)

• $\mathbf{We\ know\ the\ formula\ of\ volume\ of\ sphere=\frac{4}{3}\times \pi \times R^{3}}$

        $\mathbf{The\ volume\ of\ sphere=\frac{4}{3}\times \frac{22}{7} \times 21^{3}}$

         Means

         Volume of sphere = 38808 cm³                        ...2)

• So

• Volume of the carved out wood​ =Volume of cube -Volume of sphere

        Volume of the carved out wood​ =74088 -38808

       Volume of the carved out wood​ = 35280 cm³