A cylindrical pencil of diameter 1.2 cm has one of its end sharpened into a conical shape of height 1.4 cm. The volume of the material removed is

A. 1.057 cm³

B. 4.224 cm³

C. 1.056 cm³

D. 42.24 cm³

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\text{Required volume removed}} \cr & = \pi {r^2}h - \frac{1}{3}\pi {r^2}h \cr & = \frac{2}{3}\pi {r^2}h \cr & = \frac{2}{3} \times \frac{{22}}{7} \times .6 \times .6 \times 1.4 \cr & = 1.056{\text{ c}}{{\text{m}}^3} \cr} $$