Question

a solid metallic cylinder of length 21 cm and diameter 14 cm is melted and made into a broader and shorter cylinder of double the diameter. find its new length

Answer 1

hope this helps..........

Answer 2

Given :

A  solid metallic cylinder of length 21 cm and diameter 14 cm is melted and made into a broader and shorter cylinder of double the diameter

Find:

Find its new length

Solution:

Length of cylinder = 21 cm

diameter of cylinder = 14 cm

Radius of cylinder = $\frac{Diameter}{2}=\frac{14}{2}= 7 m$

Volume of cylinder 1 =$\pi r^2 h = \pi \times 7^2 \times 21$

We are given that cylinder is melted and made into a broader and shorter cylinder of double the diameter

So, diameter of new cylinder = 28 cm

Radius of new cylinder = $\frac{28}{2}=14 cm$

Volume of cylinder 2 =$\pi \times 14^2 \times h$

So, Volume of cylinder 1 = volume of cylinder 2

So,  $\pi \times 7^2 \times 21 =\pi \times 14^2 \times h \\7^2 \times 21 =14^2 \times h \\\frac{7^2 \times 21}{14^2}=h\\5.25= h$

Hence The height of cylinder is 5.25 cm