How many kilograms of sugar will the bigger one hold?
- Thread starter chijioke
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No - area of the bases of the cylinders are NOT equal.
But we were not required to find area. Are we?
When it comes to matter of similar solid, I am thinking of volumes rather than areas?
No - you should think about dimension (linear measurements).
Why do you say that? Just take a look at this.
Here, we asked to find volumes not area. Here is a solution provided for it.
So how do you compare or contrast this?
Dr.Peterson
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Steven G
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Are you serious? The formula for the volume of a cylinder requires you to know the area of the base. V = (pir^2)*height = (area of the base)*height
Steven G
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They might be, but you are 100% correct that we just can't assume that. Good catch.
Dr.Peterson
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No, they can't be equal, because the heights are different, and the cylinders are similar.
But we don't have to use that formula.
Why are you misleading this poor person?
Steven G
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Your correct.
Steven G
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...and what formula do you use.
Dr.Peterson
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I shall probably be sorry that I intruded on this particular thread.
What does similar mean with respect to two solids? It means that each relevant linear dimension of one solid is in the same ratio to the corresponding linear dimension of the other solid.
So, if the height of cylinder A is twice the height of cylinder B and cylinders A and B are similar, then the radius of cylinder A is twice the radius of cylinder A.
[math]h_A = 2h_B \text { and } r_A = 2r_B.\\ v_B = h_A \pi r_A^2 = 2h_B \pi (2r_B)^2 = 8h_B \pi r_B^2 = 8 v_A.[/math]
The math is trivial once you understand what “similar” means.
What does similar mean with respect to two solids? It means that each relevant linear dimension of one solid is in the same ratio to the corresponding linear dimension of the other solid.
So, if the height of cylinder A is twice the height of cylinder B and cylinders A and B are similar, then the radius of cylinder A is twice the radius of cylinder A.
[math]h_A = 2h_B \text { and } r_A = 2r_B.\\ v_B = h_A \pi r_A^2 = 2h_B \pi (2r_B)^2 = 8h_B \pi r_B^2 = 8 v_A.[/math]
The math is trivial once you understand what “similar” means.
I am thinking that since they are asking of volume of bigger drum, volume are are in three dimensions- cubes. We need to take the ratio of the heights which is linear scale factor and convert it to cube scale factor in other to find the volume of bigger drum.
Coming back to the op:
What is the relationship between mass and area as regards to this particular problem?
Yes, poor indeed as it's related to this very matter.
Yes, area is in two dimensions, while volume is three dimensions. What about that?
Steven G
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That is true. What is also true is that the VOLUME of a cylinder is BASE*height. The base is the AREA of a circle--aka the base