Question

A cone of height 7 cm and base radius 1 cm is carved from a cuboidal block of wood 10 cm × 5 cm × 2 cm. Assuming π = \(\frac{22}{7}\). What is the percentage of wood wasted in the process ?

(a) \(92\frac23\)% 

(b) \(46\frac13\)%

(c) \(53\frac23\)%

(d) \(7\frac13\)%

Answer 1

(a) \(92\frac23\)%

Volume of cone = \(\frac13\)πr²h = \(\frac13\times\frac{22}{7}\times1\times7=\frac{22}{3}\) cu. cm 

Volume of cubical block = (10 × 5 × 2) cm³ = 100 cm³

∴ Wastage of wood = \(\frac{\big(100-\frac{22}{7}\big)}{100}\times100\)

= \(\frac{278}{3}\)% = \(92\frac23\)%