The largest possible right circular cylinder is cut out from a wooden cube of edge 7 cm. Find the volume of the cube left over after cutting the cylinder (in cm). (Use $$\pi = \frac{22}{7}$$)

length of each side of wooden cube = 7 cm

volume of cube = $$\left(length\ of\ each\ side\right)^3$$

= $$7^3$$

= 343 $$cm^3$$    Eq.(i)

When the largest possible right circular cylinder is cut out from a wooden cube, then the height of the cylinder will be equal to the length of each side of the cube and the radius of the cylinder will be half of the length of each side of the cube.

height of the cylinder = 7 cm

radius of the cylinder = $$\frac{7}{2}$$ cm

volume of cylinder = $$\pi\times\left(radius\right)^2\times\ height$$

= $$\frac{22}{7}\times\left(\frac{7}{2}\right)^2\times\ 7$$

= $$\frac{22}{7}\times\frac{7}{2}\times\frac{7}{2}\times\ 7$$

= $$11\times\frac{7}{2}\times7$$

= $$3.5\times77$$

= 269.5 $$cm^3$$    Eq.(ii)

volume of the cube left over after cutting the cylinder =  Eq.(i)- Eq.(ii)

= 343-269.5

= 73.5