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)

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- Feb 23rd 2007, 12:31 AMgracychange 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 AMSoroban
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