Question

A solid iron pole consists of a cylinder of height $220cm$ and base diameter$24cm,$ which is surmounted by another cylinder of height$60cm$ and radius $8cm.$ Find the mass of the pole, given that$1c{m}^3$ of iron has approximately $8g$ mass.

Answer 1

Height of large cylinder $\left(H\right)=220cm$

Radius of large cylinder $\left(R\right)=\frac{24}{2}=12cm$

Height of small cylinder $\left(h\right)=60cm$

Radius of small cylinder $\left(r\right)=8cm$

Step1: We have to find the mass of the pole, given that $1c{m}^3$ of iron has approximately $8g$ mass.

∴ Volume of iron $=$Volume of the big cylinder $+$Volume of the small cylinder

$$\begin{gathered} ={\mathrm{\pi R}}^2\mathrm{H}+{\mathrm{\pi r}}^2\mathrm{h} \\ =\mathrm{\pi }({\mathrm{R}}^2\mathrm{H}+{\mathrm{r}}^2\mathrm{h}) \\ =3.14\times (12\times 12\times 220+8\times 8\times 60) \end{gathered}$$

$=111532.8c{m}^3$

As given $,$ Mass of $1c{m}^3=8g$

Mass for $111532.8c{m}^3=8\times 111532.8g$

$=892,262.4grams$

$=892.2624kg$