The Sparkling Soda Company has asked you to design a new can for its soda that holds the same amount but?

Question

increases its hight by 25%/ By what percent (to the nearest tenth of a percent) must the radius be decreased to accomplish this?

Answer 1

It would have to be reduced by 10.6% in other words, you would multiply the radius by .894.

The height is being multiplied by 1.25 in order to increase it by 25%. In order to keep the volume the same, you need to divided something by 1.25. We are looking to take the reduction from the radius, but notice that in the formula for the volume of a cylinder, the radius is sqaured. So we will actually multiply the radius by the square root of (1/1.25). That way, when it is squared to equal (1/1.25) it will cancel with the (1.25) that we multiplied the height by. The square root of (1/1.25) comes out to about .894 (nearest tenth of a percent) which means that we reduced the radius by 10.6%

Answer 2

Volume = height * area of circle

If the height is 5/4 the original, the circle area must be 4/5 the original, since the radius is squared we need the square root of 4/5= .894..... So the radius is 89.4% the original. So it is decreased by 10.6%

Answer 3

i think 5%... you can check it by using the formula volume=(pie)(r^2)(height)

Answer 4

u r missing info

Answer 5

pir^2*h=pR^21.25h
so r^2=R^2*1.25
r=sqrt(1.25)R
r=1.118R

Answer 6

V=pi*r1*r1*h1 = pi*r2*r2*h2
since h2=1.25*h1
pi*r1*r1*h1 = pi*r2*r2*1.25*h1
reducing ...
r2*r2=r1*r1/1.25
r2=r1/sqrt(1.25)
r2/r1=1/1.118=89.44
thus r2 is 10.557% less than r1

Answer 7

radius2^2*1.25=radius1^2

radius2=radius1/sqrt(1.25)=0.8944*radius1

10.5%