Question

If the radius of a cylinder was shrunk down to a quarter of its orignal size and the height was reduced to a third of its original size, what would be the formula to find the modified surface area?

Answer 1

Surface area, S, is

`S=2\pi r^2 + 2\pi rh`

Replace the radius with (1/4)r and the height with (1/3)h and you get the new surface area

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Answer 2

`(\pi r^2)/(8)+(1)/(6)\pi rh`

Explanation:

Let h be the original height of cylinder and r be the original radius of cylinder

According to question

`r'=(1)/(4)r`

`h'=(1)/(3)h`

Surface area of cylinder=
`2\pi r(r+h)`

Using the formula

Surface area of cylinder=
`2\pi * (1)/(4)r((1)/(4)r+(1)/(3)h)`

Surface area of cylinder=
`(\pi r^2)/(8)+(1)/(6)\pi rh`