Question

The radius of the inner surface of lead pipe is 1.5 dm and the radius of outer surface is 1.9 dm. If
the pipe be melted and formed into a solid cylinder of the same length as before, find its radius.​

Answer 1

Therefore the radius of cylinder is 1.16 dm.

Step-by-step explanation:

Given, The radius of the inner surface of lead pipe  is 1.5 dm and the radius of outer surface is 1.9 dm.

Let the height of the lead pipe be x.

Here h= x,

The  radius of outer surface is (R)= 1.9 dm

The radius of the inner surface is (r)=1.5 dm

Then the volume of the lead in the pipe is

$=\pi\times h(R^2-r^2)$

$=\pi \times x(1.9^2-1.5^2)$  dm³

$=1.36\pi x$ dm³

Let the radius of the cylinder be a.

Since the length of the cylinder is same as the length of the lead pipe.

Then the length of the cylinder is(h)=x

Therefore the volume of the cylinder =$\pi r^2 h$

                                                             = $\pi a^2x$ dm³

According to the problem,

$\pi a^2x=1.36\pi x$

$\Rightarrow a =\sqrt{1.36}$

$\Rightarrow a = 1.16$

Therefore the radius of cylinder is 1.16 dm.