# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 11 Mensuration Exercise 17.5

A hollow copper pipe of inner diameter 6 cm and outer diameter 10 cm is melted and changed into a solid circular cylinder of the same height as that of the pipe. Find the diameter of the solid cylinder.

Solution:

When we convert one solid shape to another, its volume remains the same, no matter how different the new shape is.

Given inner diameter of the pipe = 6 cm

So inner radius, r = 6/2 = 3 cm

Outer diameter = 10 cm

Outer radius, R = 10/2 = 5 cm

Let h be the height of the pipe.

Volume of pipe =π (R2-r2)h

= π (52-32)×h

= π h(25-9)

= 16π h cm3

Let r be the radius of solid cylinder.

Volume of solid cylinder = π r2h

Since pipe is melted and changed into a cylinder, their volumes remains same.

π r2h = 16π h

r2 = 16

r = 4 cm

Diameter = 2r = 2×4 = 8 cm

Hence the diameter of the cylinder is 8 cm.

Related Questions

Lido

Courses

Teachers

Book a Demo with us

Syllabus

Maths
CBSE
Maths
ICSE
Science
CBSE

Science
ICSE
English
CBSE
English
ICSE
Coding

Terms & Policies

Selina Question Bank

Maths
Physics
Biology

Allied Question Bank

Chemistry
Connect with us on social media!