Question

An iron pillar consists of a cylindrical portion $2.8m$ high and $20cm$ in diameter and a cone $42cm$ high is surmounting it. Find the weight of the pillar, given that $1c{m}^3$ of iron weighs $7.5g$.

Answer 1

Step 1: Find the volume of the pillar

Given that,

Let $h_1$ be the cylinder's height $=2.8m$ or $280cm$ $(1m=100cm)$

Let $h_2$ be the cone's height $=42cm$.

Let $d$ be the cylinder's diameter $=20cm$

Let $r$ be the cylinder's radius $r=\frac{d}{2}$ $\Rightarrow r=\frac{20}{2}=10cm$

The volume of the iron pillar $=$ Volume of the cylindrical portion $+$ Volume of the cone

The volume of the cylinder of radius $r$ and height $h_1$ $={\mathrm{\pi r}}^2{\mathrm{h}}_1$

The volume of the cone of radius $r$ and height $h_2$ $=\frac{1}{3}\pi r^2{h}_2$

Therefore, the volume of the iron pillar $=\pi r^2{h}_1+\frac{1}{3}\pi r^2{h}_2$

$$\begin{gathered} =\pi r^2\left(h_1+\frac{1}{3}{h}_2\right) \\ =\left(\frac{22}{7}\right){\left(10\right)}^2\left(280+\frac{1}{3}\left(42\right)\right) \\ =\left(\frac{22}{7}\right)\times 100\times \left(280+14\right) \\ =\left(\frac{22}{7}\right)\times 100\times \left(294\right) \\ =92400c{m}^3 \end{gathered}$$

Therefore, Volume of the iron pillar $=92400c{m}^3$

Step 2: Find the weight of the pillar.

Weight of the pillar $=\frac{Volumeofpillar\times weightofiron}{1000}$

$=\frac{92400\times 7.5}{1000}$

Weight of the pillar $=693kg$

Hence, the weight of the pillar is $693kg$