A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron has been used in making the tube?

Answer : $8792\; \text {cm}^{3}$

We know that

Volume of cylinder is given as $\pi r^{2}h$             (where r = outer radius and h is the height)

Here, length of cylinder will be considered as its height

$\left ( \text {Height=length=100 cm} \right )$

Outer diameter is given as, $d=16\; cm$

So, outer radius $r=\frac{16}{2}=8 \; cm$

Thus volume of cylinder $=\pi r^{2}h$

$=3.14 \times \left ( 8 \right )^{2}\times 100$

$=20096\; cm^{3}$

Thickness of iron sheet = 2 cm

Now, inner diameter = outer diameter – 2 (Thickness of iron sheet)

Inner diameter $=16-\left ( 2 \times 2 \right )=12\; cm$

So, inner radius $\left ( R \right )=\frac{12}{2}=6 \; cm$

Now, Volume of inner cylinder $=\pi r^{2}h$,                       (where R = inner radius)

$=\pi R^{2}h$

$=3.14 \times \left ( 6 \right )^{2}\times 100$

$=11304\; cm^{3}$

Thus, Volume of iron used = Volume of outer cylinder - Volume of inner cylinder

$=\left ( 20096-11304 \right )cm^{3}$

$=8792\; cm^{3}$

Hence the answer is $8792\; cm^{3}$

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