# Thread: Mathematically similar...work out length

1. ## Mathematically similar...work out length

Two cylinders P and Q are mathematically similar.

The total surface area of cylinder P is 90pi cm^2
The total surface area of Cylinder Q is 810pi cm^2
The length of cylinder P is 4cm

Work out the length of cylinder Q

2. I'm guessing that it is 36.

The surface area of Q divided by the surface area of P is 4. So I take P's length and times it by 4 giving me 36.

I repeat this when it tells me to work out the volume. 100pi goes to 400pi. Or is it 100x4x4?

3. Originally Posted by Mukilab
Two cylinders P and Q are mathematically similar.

The total surface area of cylinder P is 90pi cm^2
The total surface area of Cylinder Q is 810pi cm^2
The length of cylinder P is 4cm

Work out the length of cylinder Q

$\displaystyle \dfrac{810}{90} = 9$

The area has increased 9 times.

for a square:
if you double the sides you get 4 times the area.
if you triple the sides you get 9 times the area (see above)
if you quadruple the sides you get 15 times the area.
Two cylinders P and Q are mathematically similar.
Since area is defined in square units, the length has increased by $\displaystyle \sqrt{9} = 3$

If the length of cylinder P is 4 then the length of cylinder Q would be 4*3.

You can compute the radius for cylinder P from the infomation given.
Then multiply by 3 to get dimensions for cylinder Q.

Does that make sense?

.

4. Originally Posted by aidan
$\displaystyle \dfrac{810}{90} = 9$

The area has increased 9 times.

for a square:
if you double the sides you get 4 times the area.
if you triple the sides you get 9 times the area (see above)
if you quadruple the sides you get 15 times the area.

Since area is defined in square units, the length has increased by $\displaystyle \sqrt{9} = 3$
Careful here! I and, I think, most people, would interpret "increased by 3" as meaning "+ 3". It would be better to say "multiplied by 3".

[qote]If the length of cylinder P is 4 then the length of cylinder Q would be 4*3.

You can compute the radius for cylinder P from the infomation given.
Then multiply by 3 to get dimensions for cylinder Q.

Does that make sense?

.[/QUOTE]

5. "Magnified by a factor of 3" would be acceptable language in this situation.

6. Thank you for the answers although I did understand by 3...