How to Solve Cake and Pipe Equations: Helpful Tips and Solutions

[Adam Rabe]

Homework Statement

Homework Equations

Cake one...
Area of circle times height
Pipe one... Av = Av

The Attempt at a Solution

Hello, i would like some help in the right direction/
I had a go at these problems and got B) for the pipe one and C for the cake one.
However the correct answers for the pipe one is A) whereas the one for the cake is E.).

I don't understand what I am doing wrong. If you try substituting values and work backwards the constants i get don't fit.
EG: for the pipe one i made r = 4...
pi * 4^2 * 0.5 = pi* x * 4^2 * 2
x = 0.25 so i got B, but the correct answer is A...

For the cake problem i made h=5 and diametre = 8cm (radius = 4)...
pi * 4^2 * 5 = 251 m-3
i then doubled volume, and worked backwards to find factor to increase radius and therefore diamtre by...

502 = pi * r^2 * 5
r = 5.6418
5.6418/4 = 1.44... so i got C, but correct answer is E

Please help me

 

[mjc123]

Pipe: if x is the scaling of the radius, you should have pi*x^2*4^2*2
Cake: it is a scale model, so all dimensions increase by the same factor: pi*x^2*4^2*x*5 = 502

 

[Adam Rabe]

Pipe: if x is the scaling of the radius, you should have pi*x^2*4^2*2
Cake: it is a scale model, so all dimensions increase by the same factor: pi*x^2*4^2*x*5 = 502

Hello, thank you so much! I get the one with the pipe, but i don't quite get the second one, where did the other x come from? Do you have a site i can read up on to explain this I'm too stupid.

 

[haruspex]

Hello, thank you so much! I get the one with the pipe, but i don't quite get the second one, where did the other x come from? Do you have a site i can read up on to explain this I'm too stupid.

It says it is a scale model, so all dimensions increase in the same ratio. If the cake starts with radius r and height h, and all dimensions are scaled up by a factor x, what is the new radius? What is the new height? What is the new volume?