Question

An iron pillar consists of a cylindrical portion of 2.8m height and 20cm, in diameter and a cone of 45 cm height surmounting it find the weight of the pillar, if 1\[c{m^3}\] weighs 7.5g.

Answer 1

Hint – To calculate the total weight of solid figure, we need to first the volume of the given solid figure which comprises of solid cylinder and a cone and the use the density relation to obtain the total weight of the solid figure, i.e. Mass = density $\times$ volume.
Complete step-by-step answer:

Given,
Diameter of cylinder=20 cm
Therefore, radius of cylinder= $\dfrac{{20}}{2} = 10cm$
Height of cylinder=2.8m=280cm
Height of cone=45cm
Radius of cone=10cm …..(as the cone surmounts the cylinder)
Volume of the solid figure= volume of cylinder + volume of cone
Volume of cylinder= $\pi {r^2}h$
$
  \dfrac{{22}}{7} \times {(10)^2} \times 280 \\
   = 88000c{m^3} \\
$
Volume of cone=$\dfrac{1}{3}\pi {r^2}h$
$
  \dfrac{1}{3} \times \dfrac{{22}}{7} \times {(10)^2} \times 45 \\
   = 4714.3c{m^3} \\
$
Total volume of figure= volume of cylinder + volume of cone
=88000+4714.3
=92714.3$c{m^3}$
We know the relation, $Mass = density \times volume$
Therefore total weight of figure, W=$density \times volume$
W=\[7.5 \times 92714.3\]
\[
   = 695357.25g \\
   = 695.357kg \\
\]
Hence the answer to this question is 695.357kg.
Note – To solve such a question we must remember the relation of density and the conceptual knowledge of its application to find the weight of a given volume of a solid figure and the basic formulae of solid figures.