Question

An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that 1 cm³ of iron weights 7.5 g.

Answer 1

Height of the cylindrical portion of the iron pillar, h = 2.8 m = 280 cm
Radius of the cylindrical portion of the iron pillar, r = 20 cm
Height of the cone which is surmounted on the cylindrical portion, H = 42 cm
Now, volume of the pillar = volume of the cylindrical portion + volume of the conical portion
= $\mathrm{\pi }{r}^{\mathit{2}}h+\frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}H$
$$\begin{gathered} =\frac{22}{7}\times {10}^2\left(280+\frac{1}{3}\times 42\right) \\ =\frac{22}{7}\times \left(280+14\right) \\ =\frac{22}{7}\times 100\times 294 \\ =92400{\mathrm{cm}}^3 \end{gathered}$$

∴ Weight of the pillar = volume of the pillar $\times$ weight per cubic cm
$$\begin{gathered} =92400\times \frac{7.5}{1000} \\ =693\mathrm{kg} \end{gathered}$$