Question

An iron pipe is 42 cm long and its exterior radius is 4 cm. If the thickness of the pipe is 1 cm and iron weights $100g/c{m^3}$ the weight of the pipe is
A. 92.4 kg
B. 211.2 kg
C. 189.34 kg
D. 118.8 kg

Answer 1

Hint: In this question, we have a hollow pipe whose exterior radius is 4 cm. Its thickness is 1 cm. To find an internal radius we subtract the exterior radius and thickness of the pipe. Now we will find the volume of hollow pipe using this formula $\pi \left( {R - r} \right)l$. Then we will multiply the volume with $100g/c{m^3}$to find the weight of the pipe. We get the answer in grams so we will convert it in kilograms by dividing the weight by 1000.

Complete step-by-step answer:
Given,
Length of the iron pipe = 42 cm
Its exterior radius = 4 cm
Thickness of the pipe = 1 cm
Then internal radius = Exterior radius – Thickness of the pipe
                                     = 4 cm – 1 cm = 3 cm
Weight of the iron = $100g/c{m^3}$
Thus, the volume of iron pipe = External Volume – Internal Volume
$ = \pi \left( {{R^2} - {r^2}} \right)l$ where R = exterior radius, r = internal radius and l = length
$ = \dfrac{{22}}{7}\left( {{4^2} - {3^2}} \right)42$
$ = 924c{m^3}$
We have, Weight of an object = Volume × Density
Hence, the weight of the pipe = 924 X 100 = 92400 g
Weight of the pipe in kilogram $ = \dfrac{{92400}}{{1000}} = 92.4$kg
Therefore, weight of the pipe is 92.4 kg

So, the correct answer is “Option A”.

Note: In a hollow pipe, we have two radii, one is internal radius and another one is external radius. Volume of a solid cylinder is \[\pi {r^2}h\]. Volume of the hollow cylinder means volume of amount present in cylinder and can deduce this by finding volumes of cylinders and subtract the volume with smaller radius from the volume of larger radius and it will be $\pi \left( {{R^2} - {r^2}} \right)l$, where R is bigger radius and r be smaller radius.