# change in volume

• Feb 23rd 2007, 12:31 AM
gracy
change in volume
The radius of cylinder is reduced by 4% and its height is increased by 2%, determine the approximate percentage changed in (i) its volume (ii) its curved surface area (neglecting the product of small quantities)
• Feb 23rd 2007, 03:26 AM
Soroban
Hello, Gracy!

I'll assume that this is to be done by Arithmetic . . .

Quote:

The radius of cylinder is reduced by 4% and its height is increased by 2%.
Determine the approximate percentage changed in (i) its volume
(ii) its curved surface area (neglecting the product of small quantities)

Let r be the original radius, then 0.96r is the new radius.
Let h be the original height, then 1.02h is the new height.

The original volume is: .V1 .= .πr²h

The new volume is: .V2 .= .π(0.96r)²(1.02h) . .(0.94)πr²h

The change in volume is: .V1 - V2 .= .πr²h - (0.94)πr²h .= . (0.06)πr²h

. . . . . . . . . . . . . . . . .change . . . (0.06)πr²h
Percent of change . = . --------- .= .------------- .= .0.06 .= .6%
. . . . . . . . . . . . . . . . .original . . . . .πr²h

You can do part (ii).
The curved surface area is: .S .= .2πrh