Question

The largest possible sphere is carved out of a cube of side 7 cm. Find the volume of wood left.

Answer 1

Hint: This is a problem of volumes. One should know the formula for the volume of cube and sphere. They are given by-

$$\begin{gathered} \mathrm{V}\left(\mathrm{cube}\right)=\mathrm{side}\times \mathrm{side}\times \mathrm{side} \\ \mathrm{V}\left(\mathrm{sphere}\right)={\displaystyle \frac{4}{3}}{\mathrm{\pi }\mathrm{r}}^3 \end{gathered}$$

 To solve this problem, we will find the volume of the cube and largest sphere, then subtract them.

Complete step-by-step answer:

This is a front view of the figure. We can clearly see that the radius of the sphere is half the side of the cube, so radius of the sphere is r = 3.5 cm.


Volume of the cube = (side)3 = 73 = 343 cm3

Volume of sphere =

$$\begin{gathered} ={\displaystyle \frac{4}{3}}\times {\displaystyle \frac{22}{7}}\times 3.5\times 3.5\times 3.5 \\ =179.66{\mathrm{cm}}^3 \end{gathered}$$

The volume of wood left = 343 -179.66 = 163.33 cm3


This is the required answer.

Note: To solve such problems, making a diagram is necessary and helpful, because using the diagram, we easily found the radius of the square. Also, do not forget to write the units in the answer.