Question

If 1sq. cm iron weight 21g. Find the weight of a cast pipe of length 1m with a bore of radius 3cm in which the thickness of the metal is 1cm.

Answer 1

Hint:Let us take the length of a cylinder \[h\], the radius is \[r\].
So, the total surface area of the pipe\[ = \pi {r^2}h + \pi {r^2}\]

Formula used:The total surface area of cylinder is \[ = \pi {r^2}h + \pi {r^2}\]

Complete step-by-step answer:
As per the given question,
The length of the pipe is \[1\]m.
We know that, \[1\]m\[ = 100\]cm
So, the length of the pipe is \[ = 100\]cm.
The radius of the bore is \[3\]cm. it means the outer radius of the pipe is \[3\]cm.
The thickness of the metal is \[1\] cm.
So, the inner radius is \[ = 3 - 1 = 2\] cm.
Now, we will find the total surface area of the pipe with length\[ = 100\]cm and outer radius\[ = 3\]cm.

Substitute the value of \[h = 100\& r = 3\]in the general equation of the total surface area of a pipe we get,
\[{A_1} = \pi {3^2} \times 100 + \pi {3^2} = 909\pi \]
Next, we will find the total surface area of the pipe with length\[ = 100\]cm and outer radius\[ = 2\]cm.
Substitute the value of \[h = 100\& r = 2\]in the general equation of the total surface area of a pipe we get,
\[{A_2} = \pi {2^2} \times 100 + \pi {2^2} = 404\pi \]
So, the area of the iron of the pipe \[{A_1} - {A_2}\]
Substitute the values of \[{A_1},{A_2}\] we get,
\[909\pi - 404\pi = 505\pi \]sq. cm
It is also given that, \[1\] sq. cm iron weight \[21\]g.
So, weight of \[505\pi \]sq. cm is \[505\pi \times 21\]g
Substitute the value of \[\pi = \dfrac{{22}}{7}\] we get,
The total weight is \[505 \times \dfrac{{22}}{7} \times 21\]g
Multiplying we get,
\[ = 33,330\]g
We know that, \[1\]kg \[ = 1000\]g
So, \[33,330\]g\[ = \dfrac{{33,330}}{{1000}}\]kg\[ = 33.33\]kg
Hence,
The weight of the pipe is \[33.33\]kg

Note:We can find the total area of the pipe in another way.
Let us take the length of a cylinder \[h\] , the outer radius is \[R\] and the inner radius is \[r\].
So, the total surface area of the pipe\[ = \pi ({R^2} - {r^2})h + \pi ({R^2} - {r^2})\]
Substitute \[h = 100,R = 3,r = 2\] we get,
The area \[ = \pi ({3^2} - {2^2}) \times 100 + \pi ({3^2} - {2^2}) = 505\pi \]