a height of 20 in. explain. thanks.
2007-03-14 06:55:42 · 6 answers · asked by catmuffin 1 in Science & Mathematics ➔ Engineering
As we know the volume of a cylinder is given by the formula
pi*r^2*h,where r is the radius of the circular base and h is the height of the cylinder.Now,if we donot take into account,the value of pi which is common to both the cylinders,the volume of the two cylinders in question will be in the ratio of radius^2* h of the respective cylinders
In the first cylinder r^2*h
=20^2*16
400*16
=6400
in the second cylinder r^2h
=16^2*20
=256*20
=5120
kAs 6400 is greatr than 5120,the first cylinder will have more volume than the second cylinder
This problem may also be solved by calculating the volume of the first and second cylinder separately and showing that the first cylinder has more volume than the second one
2007-03-14 18:33:43 · answer #1 · answered by alpha 7 · 0⤊ 0⤋
Diameter of a circle is a tricky thing, compared to a square. In a square, if you double it's height, it still stays the same width as it was before. With a circle, if you double its size, you're doubling it in ALL directions, not just one, no matter where you measure it. So adding a small amount to the diameter of a circle affects all directions. Depending on how much math you've had, you may recognize the growth of a circle as "exponential".
One last example/rule of thumb that helps out a lot in explaining this. With a square, if you double its width, that will double its area. With a circle, if you double its width, that will QUADRUPLE its area.
From here, you should be able to apply it and understand how an equal change to height and diameter can give you drastically different results.
2007-03-14 14:07:53 · answer #2 · answered by Erik 2 · 0⤊ 0⤋
If you can't imagine it mathematically, think of it visually---a cyinder or stack of quarters has a larger radius, hence a larger volume than a stack of dimes of the same height.
2007-03-14 14:22:01 · answer #3 · answered by Bambolero 4 · 0⤊ 0⤋
Look at the formula for volume V = PI*(r^2)*h.
radius, r, appears as a square, whereas h is linear (ie to the power of one). Therefore the value of r influences the volume more strongly than h.
2007-03-14 14:00:38 · answer #4 · answered by dudara 4 · 3⤊ 0⤋
Volume increases proportional to height (to the power of 1), but proportional to radius-SQUARED.
which one goes up faster? to the power of 1, or power of 2?
.
2007-03-14 14:03:40 · answer #5 · answered by tlbs101 7 · 1⤊ 0⤋
first of all, you need to know the terms and what they mean. Once you understand the terms radius, and height, it will be much clearer.
2007-03-14 16:33:38 · answer #6 · answered by minorchord2000 6 · 0⤊ 0⤋