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)
Hello, Gracy!
I'll assume that this is to be done by Arithmetic . . .
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