volume of a cylinder

9/12/2016 7:36:50

   

brojenbhatta
Point: 1
New Member

A hollow cylinder of outer diameter 14 cm and height 28 cm is melted to form a new hollow cylinder of outer radius 14 cm and of the same thickness. Find the height of the new cylinder.

7/29/2017 17:10:0

   

Yang
Point: 148
Junior Member

the old hollow cylinder volume:
V1 = pi * outer radius^2 * height - pi * inner radius^2 * height
V1 = pi * height * (outer radius^2 - inner radius^2)
V1 = pi * 28cm * (7cm^2 - inner radius^2)

thickness = outer radius - inner radius

the new hollow cylinder volume:
V2 = pi * new outer radius^2 * height - pi * new inner radius^2 * height
V2 = pi * height * (14cm^2 - new inner radius ^2)

you know that the thickness is the same, thus the new inner radius will be:
the old inner radius + the increase (7cm)

now the equation becomes:
V1 = V2
pi * 28cm * (7cm^2 - old inner radius^2) = pi * new height * (14cm^2 - (old inner radius + 7cm)^2)

now you will need to subtract the h.