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?

Answers (1)

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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