Okay, I don't know how to do this. My teacher is having us do this standardized test thing in our textbook when he hasn't taught us how to do the problems in it. He doesn't teach well at all, but anyways. I could really use someones help. How do you find the ratio of the volume of a cylinder to the volume of another cylinder? okay here is the question in my text: "Every dimension of cylinder A is multiplied by 4 to make cylinder B. WHat is the ratio of the volume of cylinder A to the volume of cylinder B?"
Okay The base of Cylinder A is 3 and the height is 5. BTW I'm actually pretty good at math when someone can teach it to me correctly. Please HELP ME!
Okay The base of Cylinder A is 3 and the height is 5. BTW I'm actually pretty good at math when someone can teach it to me correctly. Please HELP ME!
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All dimension of cylinder A x 4 =
Radius x 4, let the old radius be r, new radius be 4r
Diameter x 4,
H x 4, let the old height be h, new height be 4h
π stay the same
V = πr²h
Cylinder A has a volume of πr²h
Cylinder B has a volume of π(4r)²(4h)
= π16r²4h
= (16)(4)πr²h (according the commutative property of multiplication which states 2 x 3 = 3 x 2)
= 64 πr²h
Cylinder A : Cylinder B = πr²h : 64 πr²h
= 1 : 64
Disregarding the actual dimensions of the original cylinder, the ratio of cylinder A to B is 1 : 64 or in fraction form, 1/64.
Radius x 4, let the old radius be r, new radius be 4r
Diameter x 4,
H x 4, let the old height be h, new height be 4h
π stay the same
V = πr²h
Cylinder A has a volume of πr²h
Cylinder B has a volume of π(4r)²(4h)
= π16r²4h
= (16)(4)πr²h (according the commutative property of multiplication which states 2 x 3 = 3 x 2)
= 64 πr²h
Cylinder A : Cylinder B = πr²h : 64 πr²h
= 1 : 64
Disregarding the actual dimensions of the original cylinder, the ratio of cylinder A to B is 1 : 64 or in fraction form, 1/64.
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Its really not that hard.
Height of Cylinder A = 5
So,
Height of Cylinder B = 4(5) = 20
(I am assuming that by base you mean diameter, not that it matters, its just so that you can understand it)
Diameter of Cylinder A = 3
Diameter of Cylinder B = 4(3) = 12
Volume of cylinder A = πd²h / 4 = π (9) 5 / 4 = 45π/4 (Do not calculate it, we are going to take ratio and anything common will be slashed off)
Volume of cylinder B = πd²h / 4 = π (144) 20 / 4 =
Ratio of volumes = Volume of A / Volume of B = 45π/4 / (π (144) 20 / 4) = 1 / 64
Hope it helps...
Height of Cylinder A = 5
So,
Height of Cylinder B = 4(5) = 20
(I am assuming that by base you mean diameter, not that it matters, its just so that you can understand it)
Diameter of Cylinder A = 3
Diameter of Cylinder B = 4(3) = 12
Volume of cylinder A = πd²h / 4 = π (9) 5 / 4 = 45π/4 (Do not calculate it, we are going to take ratio and anything common will be slashed off)
Volume of cylinder B = πd²h / 4 = π (144) 20 / 4 =
Ratio of volumes = Volume of A / Volume of B = 45π/4 / (π (144) 20 / 4) = 1 / 64
Hope it helps...
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when dimensions are multiplied by 4 you are enlarging the cylinder by a scale factor of 4. Volume being 3 dimensional, the volume is multiplied by 4^3=64 so the ratio of the volume of A to volume of B =1:64
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the ratio of the volume of cylinder A to the volume of cylinder B is (the volume of cylinder A) / (the volume of cylinder B)
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We have 3 dimensions, all multiplied by 4. In the case of a circle, the 2 dimensions are kind of obscure.
If you were to take the area of the base pi(3/2)^2, you would get 9pi/4. Multiply that by 16 (4x4) and you will get 36pi. Multiply that by 20 (5x4) and you get 720pi. Compare that to the volume of the original which is 9pi/4 * 5 and you get (45pi/4)/(720pi) which comes out to 1/64.
You could have also worked this out by taking the initial volume (45pi/4) and multiplying it by 4 for every one of the three dimensions (4x4x4) to get the second volume. Then just make a ratio of the volumes (45pi/4)/(720pi/4) = 1/64 and that's the answer.
If you were to take the area of the base pi(3/2)^2, you would get 9pi/4. Multiply that by 16 (4x4) and you will get 36pi. Multiply that by 20 (5x4) and you get 720pi. Compare that to the volume of the original which is 9pi/4 * 5 and you get (45pi/4)/(720pi) which comes out to 1/64.
You could have also worked this out by taking the initial volume (45pi/4) and multiplying it by 4 for every one of the three dimensions (4x4x4) to get the second volume. Then just make a ratio of the volumes (45pi/4)/(720pi/4) = 1/64 and that's the answer.