Question

A solid cone of radius 5cm and height 14cm is melted and recast into a pipe. The outer radius and thickness of the pipe are 4cm and 1cm respectively. Find the length of the pipe.

Answer 1

Given:

A solid cone of radius 5cm and height 14cm is melted and recast into a pipe. The outer radius and thickness of the pipe are 4cm and 1cm respectively

To find:

The length of the pipe.

Solution:

We know that in the case of the melting and recast any of the solid the volume of the solid in both cases remains the same.

Volume of Cone = Volume of the pipe

1/3πr²h = π(R²-R'²)H

where the parameters are:

r = 5 cm

h = 14 cm

R = 4 cm

R' = 4-1 = 3 cm

By putting the values we get:

• 1/3πr²h = π(R²-R'²)H
• 1/3(5)²×14 = (4²- 3²)H
• 350/3 = 7H
• H = 50/3
• H = 16.67 cm ( approx.)

So,

The length of the pipe is 16.67 cm