Question

The dimensions of cylinder B are 5 times the dimensions of cylinder A.

If the surface area of cylinder A is 50 cm2, what is the surface area of cylinder B?

Answer 1

Mmm what's the formula for Surface Area of a Cylinder?
Lemme try to remember...\[\Large\bf\sf SA\quad=\quad \pi r^2+2\pi r h\]Mmm ya I think that's right, yes?

Answer 2

\[\Large\bf\sf SA_A\quad=\quad \pi r^2+2\pi r h\]\[\Large\bf\sf 50\qquad=\quad \pi r^2+2\pi r h\]

There is our surface area for A.

Answer 3

\[\Large\bf\sf SA_B\quad=\quad \pi(5r)^2+2\pi(5r)(5h)\]In cylinder B, all of our dimensions have been scaled up by a factor of 5.
So we replace all of the r's with 5r's.
And we replace all of the h's by 5h's.

Answer 4

Multiplying some stuff out gives us,
\[\Large\bf\sf SA_B\quad=\quad 25\pi r^2+25\cdot2\pi r h\]Factor a 25 out of each term,\[\Large\bf\sf SA_B\quad=\quad 25(\color{royalblue}{\pi r^2+2\pi r h})\]That blue part should look really familiar :O