math help!?

Question

A company is decreasing by 10 percent the amount of tuna sold in cylindrical cans. The cans will have the same height but a smalller diameter to minimize the impact on consumers when they see the smaller cans. By how much should the diameter be decreased to accomodate the change?

Could someone please explain how to do this problem. Thank you so much.

Answer 1

A can is basicly a cylinder, the volume of a cylinder is

height * pi * radius squared

Since the height and pi are constant you only need to deal with the radius of the can. You want to decrease it's volume by 10% Therefore you need to calculate the radius where it's square is 90% of the square of it's current value.

For simplicity lets say the current radius is 10 "units" -- it doesn't matter what the units are. Therefore the radius squared would be 100 units. So we need to calculate what value would be 90 units when squared -- our new radius would be the square root of 90 units or 9.4868 units.

The new radius would be (9.4868/10) times the current radius or .94868 r.

I hope this helps.

Answer 2

in order to decrease the diameter of the can by 10% you need to multiply by 0.1 to find the difference of 10% compared to the diameter of the can.

Ex/ size of the can=H H x 0.1 = D
Difference=D H - D = new H

Answer 3

V = π r² h
r = √ (V / πh)
d = 2√(V / πh) (this is the diameter of the can before reducing)

the volume is decreased by 10%
V = (π r² h) - .1(π r² h)
V = .9(π r² h)
r = √(10V / 9πh)
d = 2√(10V / 9πh) (this is the diameter of the can after reducing)

percent = (new amount - initial amount) / initial amount * 100
percent = [ 2√(10V / 9πh) - 2√(V / πh) ] / 2√(V / πh) * 100
percent = -5.1316%

so the diameter is reduced by 5.1316%

or the diameter now is only 94.8684% of the origional diameter

Answer 4

whats the original diameter. When u have the original multiply the original diameter by 0.1then subtract that from the original diameter. Then u have ur answer.

Answer 5

Vc = pid^2h/4 for current can
Vn = pi d1^2h/4 for new can

Vn/Vc = d1^2/1^2 =.9
d1^2/d^2 = .9
d1/d2 = sqrt(.9) = .94868
So the diameter must be reduced to 94.87% of its original size.

Answer 6

cylinder volume = 3.14 x r^2 x height

since the height being keep the same then

new volume/old volume = r(new)^2 / r(old)^2 =.9

then r(new)= r(old) x 0.81

new radius for the new can will be 81% of the old can

Answer 7

you need to give people more information to answer this question =]