Answer:
The surface area of a cylinder is given by :
SA=[tex]2 \pi rh+2\pi r^{2}[/tex]
When the base is same but the height is doubled. Doubling the height replaces h with 2h:
New formula becomes:
SA=[tex]2 \pi r(2h)+2\pi r^{2}[/tex]
SA = [tex]4\pi rh+2\pi r^{2}[/tex]
We can see that only the height is doubled not the radius. The formula changes a little bit.
We can take an example-
Lets say the height of cylinder is 10 cm and radius is 4 cm
So, SA in 1st case :
SA=[tex]2\times3.14\times4\times10+ 2\times3.14\times (4)^{2}[/tex]
=[tex]251.2+100.48=351.68[/tex] cm square
SA in 2nd case:
[tex]4\times3.14\times4\times10+ 2\times3.14\times(4)^{2}[/tex]
= [tex]502.4+100.48=602.88[/tex] cm square
We can see that area of lateral surface doubles up in case 2 but the base area remains the same.
