Question 542539: If the dimensions of the following cylinder are tripled, what will be the volume of the new cylinder? dimensions are 12 and 15
Options:
15,260.4 cm3
45,781.2 cm3
61,041.6 cm3
183,124.8 cm3
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! The problem is not clearly stated, but I probably know what you mean.
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The formula for the volume of a right vertical cyclinder is the area of the circle that is the cross-section times the height of the cylinder.
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Let r = radius of the cross-section (circle)
Let h = the height of the cylinder
Let A = the area of the circle
Let V = the volume of the cylinder
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A = pi * r^2
V = A * h
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V = pi * r^2 * h
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Abstract discussion: given the formula, what happens if the the r and h dimensions are tripled? Make it easy on yourself, imagine r = 1 and h = 1:
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V = pi * 1^2 * 1
V = pi
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If we triple the dimensions, we will have 3 * 3 * 3 = 27 times the size of the original cylinder (recall, the r term is squared), or:
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we have the original V = pi cylinder multiplied by 27
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The problem gives us the dimensions of 12 and 15, but does not specify which is the radius of the circular cross section and which is the height of the cylinder. The only thing to do is to solve it both ways (Note: it matters which is which because the radius is squared and the height is not). Likely, only one of these will show up on your list of potential solutions.
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Original cylinder:
Let r = 12
Let h = 15
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You can solve for V, the volume of the original cylinder, and then multiply by 27, OR, you can triple the dimensions now and then solve for the new volume, V. Either way will provide the same answer.
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New cylinder:
Let r = 12 * 3 = 36
Let h = 15 * 3 = 45
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V = pi * 36^2 * 45
V = 183,217.68 cm^2
This result is close to one of your solutions, but not close enough.
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Reverse r and h:
Let r = 15 * 3 = 45
Let h = 12 * 3 = 36
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V = pi * 45^2 * 36
V = 229,022.10 cm^2
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This result is not on your list either.
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Please go back and check your given set of possible solutions, it seems none is the correct one.
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Cheers,
Lee
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