Question

The figure shows a metal pipe of length 35 cm.
The internal and external diameters of the pipe
are 20 mm and 28 mm respectively. Find the volume
of metal used in making the pipe, giving your
answer in cubic centimetres.
20 mm
28 mm
35 cm

Answer 1

Given:

The length of the metal pipe i.e., height "h" = 35 cm

The internal diameter = 20 mm = 2 cm

The external diameter = 28 mm = 2.8 cm

To find:

The volume  of metal used in making the pipe

Formula Used:

$\boxed{Volume\: of\:cylinder = pi\:* r^2\:*\: h}$

Solution:

Let "r" be the internal radius and "R" be the external radius.

We know,

Radius = $\frac{Diameter}{2}$

∴ Internal Radius, r = $\frac{2}{2}$ = 1 cm

and

∴ External Radius, R = $\frac{2.8}{2}$ = 1.4 cm

Now, by using the above formula, we get

The volume of the metal used in making the pipe is,

= [External Volume of the pipe] - [Internal Volume of the pipe]

= [πR²h] - [πr²h]

= πh [R² - r²]

= $\frac{22}{7}\: *\: 35 \:*\:[1.4^2\:-\:1^2]$

= $\frac{22}{7}\: *\: 35 \:*\:[1.96\:-\:1]$

= $\frac{22}{7}\: *\: 35 \:*\:0.96$

= 105.6 cm³

Thus, the volume  of the metal used in making the pipe is 105.6 cm³.

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