Say I have a cylinder of 135 kilo-grams and a radius of 2 meters. If a smaller cylinder is cut with a a radius of 1 meter, what is the mass of this smaller cylinder?
2006-10-24 15:55:34 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
m1:m2=r1^2:r2^2
135:x=4:1
x=135/4=33.75
mass of the smaller cylinder=33.75 kg
2006-10-24 15:58:47 · answer #1 · answered by raj 7 · 0⤊ 0⤋
Mass is proportional to volume, and the volume of a cylinder is proportional to the square of the radius, because V = pi*(r^2)*h. So if you halve the radius and keep the height the same (which I assume, although it is not stated), the factor of change in the mass is (1/2)^2 = 1/4. So the mass is (135 kg)*1/4 = 33.75 kg.
2006-10-24 23:00:19 · answer #2 · answered by DavidK93 7 · 0⤊ 0⤋
Volume of big= pi*r^2*h =pi*4*h
volume of small=pi*r^2*h=pi*1*h
ratio of small to big = 1 to 4.
so assuming the mass is equally distributed throughout, the mass of the smaller should be 135 divided by 4 or 33.75 kg
Hope that helps!
2006-10-24 22:59:54 · answer #3 · answered by D 3 · 0⤊ 0⤋
assuming both have the same lengths.....
find the ratio of the big circle to the small circle...
area of #1 = pix2^2 = 4pi
area of #2 = pix1^2 = 1pi
so with same lengths, cyclindar 2 will always be 1/4th the size of the larger one.
135/4 = 33.75
2006-10-24 23:02:59 · answer #4 · answered by JLEETZ 2 · 0⤊ 0⤋