Question

A cylinder has a radius r and a length l. if the radius were to double and the length were to stay the same, by what factor would the surface area change?

Answer 1

Step-by-step explanation:

Given

radius of cylinder is r and length l

If radius is doubled and length remain same

Surface area of cylinder is
`A_1=2\pi rL`

New Surface area
`A_2=2\pi (2r)L`

Percentage change in Surface area
`=(A_2-A_1)/(A_1)* 100`

`=(2\pi (2r)L-2\pi (r)L)/(2\pi (r)L)* 100=100 \%`

Answer 2

double

Step-by-step explanation:

radius = r

length = l

Surface area, A = 2 π r l .... (1)

Now the radius is doubled = 2r

length is same

Surface area, A' = 2 x π x 2 r x l

A' = 2 x 2πrl

A' = 2 A (from equation (1)

Thus, the surface area is doubled.