Difficulty Solving a Question on Volumes: concrete cube 10m x 10m x 10m & elephant

[Rambling]

Difficulty Solving a Question on Volumes: concrete cube 10m x 10m x 10m & elephant

Hi - New member so pleae go easy

I am having fantastic trouble solving a geometry challenge, to the point where I don't know anymore if it's down to a simple equation or something alot more complex. I'm hoping that someone more seasoned in the world of math can shed some light for me.

Suppose that in order to prevent an angry elephant from breaking down a door, I need to construct a concrete cube 10m x 10m x 10m to counteract the force of the elephant pushing against it.

I soon realise that I need to provide a chanel for the elephant to receive food and water, and go about drilling a cylinder with a diameter of 0.4m.

I need to calculate:

- The volume of the cube
- The volume of the cylinder
- The difference beteen the two (volume lost)
- By how much the edges of the cube must increase to make up for the lost concrete


Further things that I need to consider:

- The concrete must remain a regular cube in that each side must increase by the same amount.
- The diameter of the cylinder must remain the same but must increase with the length of the cube (so that objects can pass through the cube)
- The minimum cube size must be constructed to save cost of materials.


The orignal cube sizes provided are to two decimals but I have simplified it for myself just to try to understand the method.

I have calcuated the volume of the concrete cube 10m³ = 1000m³

I have calculated the volume of the cylinder: pi r² x L = 125.66

And the remaining block: 874.34m³

From here every way that I go I come to a dead end. I think the problem is the ever increasing cylinder.

I'd be most grateful if anyone could start me off on the way. I've attached a (crude) sketch to illustrate the issue.


Thanks for your time..

Tom.

 

[Steven G]

Hi - New member so pleae go easy

I am having fantastic trouble solving a geometry challenge, to the point where I don't know anymore if it's down to a simple equation or something alot more complex. I'm hoping that someone more seasoned in the world of math can shed some light for me.

Suppose that in order to prevent an angry elephant from breaking down a door, I need to construct a concrete cube 10m x 10m x 10m to counteract the force of the elephant pushing against it.

I soon realise that I need to provide a chanel for the elephant to receive food and water, and go about drilling a cylinder with a diameter of 0.4m.

I need to calculate:

- The volume of the cube
- The volume of the cylinder
- The difference beteen the two (volume lost)
- By how much the edges of the cube must increase to make up for the lost concrete


Further things that I need to consider:

- The concrete must remain a regular cube in that each side must increase by the same amount.
- The diameter of the cylinder must remain the same but must increase with the length of the cube (so that objects can pass through the cube)
- The minimum cube size must be constructed to save cost of materials.


The orignal cube sizes provided are to two decimals but I have simplified it for myself just to try to understand the method.

I have calcuated the volume of the concrete cube 10m³ = 1000m³

I have calculated the volume of the cylinder: pi r² x L = 125.66

And the remaining block: 874.34m³

From here every way that I go I come to a dead end. I think the problem is the ever increasing cylinder.

I'd be most grateful if anyone could start me off on the way. I've attached a (crude) sketch to illustrate the issue.


Thanks for your time..

Tom.

I have a bit confused. You wrote I have calculated the volume of the concrete cube 10m³ = 1000m³. How can 10 cubic meters equal 1000 cubic meters?

Here is what you do. Let each side of the cube increase by s, so each side is now (10+s)m. Calculate the volume of the cube, Calculate the volume of the tube. Subtract the two and set that result to 1000m³. Then solve for s.

 

[lev888]

I would try an equation:
V1(x) - V2(x) = 1000, where x is the new edge length, V1 - volume of the cube, V2 - volume of the cylinder, as functions of x.

 

[tkhunny]

Hi - New member so pleae go easy

I am having fantastic trouble solving a geometry challenge, to the point where I don't know anymore if it's down to a simple equation or something alot more complex. I'm hoping that someone more seasoned in the world of math can shed some light for me.

Suppose that in order to prevent an angry elephant from breaking down a door, I need to construct a concrete cube 10m x 10m x 10m to counteract the force of the elephant pushing against it.

I soon realise that I need to provide a chanel for the elephant to receive food and water, and go about drilling a cylinder with a diameter of 0.4m.

I need to calculate:

- The volume of the cube
- The volume of the cylinder
- The difference beteen the two (volume lost)
- By how much the edges of the cube must increase to make up for the lost concrete


Further things that I need to consider:

- The concrete must remain a regular cube in that each side must increase by the same amount.
- The diameter of the cylinder must remain the same but must increase with the length of the cube (so that objects can pass through the cube)
- The minimum cube size must be constructed to save cost of materials.


The orignal cube sizes provided are to two decimals but I have simplified it for myself just to try to understand the method.

I have calcuated the volume of the concrete cube 10m³ = 1000m³

I have calculated the volume of the cylinder: pi r² x L = 125.66

And the remaining block: 874.34m³

From here every way that I go I come to a dead end. I think the problem is the ever increasing cylinder.

I'd be most grateful if anyone could start me off on the way. I've attached a (crude) sketch to illustrate the issue.


Thanks for your time..

Tom.

What is the prize for defeating this challenge?

Original Cube:
S = 10m
Volume = S^3 = ??

Original Tube:
pi * ((0.4/2)m)^2 * S = ?? -- You will want to do this over.


New Cube:
s = S+L = 10m + a little.
Volume = s^3 = ??

New Tube:
pi * ((0.4/2)m)^2 * (S+L) = pi * ((0.4/2)m)^2 * s = ??

I was bored. Let's see if you have enough hints.