Question

A solid iron pole having cylinder portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high Find the mass of the pole , given that the mass of$1{cm}^2$ of iron is 8 gm.

Answer 1

Given radius of cylinderical part (r) = 12/2 = 6 cm

Height of cylinder (h) 110 cm

Length of cone (l) 9 cm

Volume of cylinder = $\pi r^{2}h$

$V_1=\pi (0{)}^{2}110c{m}^3........(1)$

Volume of cone = $\frac{1}{3}\pi r^{2}l$

$V_2=\frac{1}{3}\pi (6{)}^{2}9=108\pi c{m}^3...........(2)$

Volume of pole = (1)+ (2)

$V=V_1+V_2$

$\Rightarrow V=\pi (6{)}^{2}110+108\pi$

$\Rightarrow V=12785.14c{m}^3$

Given mass of $1c{m}^3$ of iron = 8 gm

Mass of $12785.14c{m}^3$ of iron

$=12785.14\times 8$

$=102281.12$

$=102.2kg$

$\therefore$ Mass of pole for $12785.14c{m}^3$ of iron is 102.2 kg