Question

*** PLEASE HELP ASAP

two cylinders have the same size base, but one is twice as tall. explain why the taller cylinder does not have double the surface area.​

Answer 1

The top isn't closed.

Explanation:

The bottom is enclosed, creating more surface area, but the top is opened.

Answer 2

The surface area of a cylinder is given by :

SA=
`2 \pi rh+2\pi r^(2)`

When the base is same but the height is doubled. Doubling the height replaces h with 2h:

New formula becomes:

SA=
`2 \pi r(2h)+2\pi r^(2)`

SA =
`4\pi rh+2\pi r^(2)`

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=
`2*3.14*4*10+ 2*3.14* (4)^(2)`

=
`251.2+100.48=351.68` cm square

SA in 2nd case:

`4*3.14*4*10+ 2*3.14*(4)^(2)`

=
`502.4+100.48=602.88` cm square

We can see that area of lateral surface doubles up in case 2 but the base area remains the same.