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

73.5

We know that,

Volume of cube = side³

Volume of cylinder = πr²h

We have,

Edge of cube = 7 cm

Volume of cube =  7³ = 343 cm³

When the largest possible right circular cylinder is cut out from a wooden cube then,

Height of cylinder = Edge of cube = 7 cm

Radius of cylinder = \(\frac{7}{2}\)cm

Volume of cylinder = π × r² × h = \(\frac{22}{7}\) × \(\frac{7}{2}\) × \(\frac{7}{2}\) × 7 =  269.5 cm³

Remaining volume = 343 - 269.5 = 73.5 cm³