SOLUTION: the volume of a cylinder is 80 cubic centimeters. if the diameter and height of the cylinder are multiplied by 4/5, what is the volume of the new cylinder?

Algebra ->  Volume -> SOLUTION: the volume of a cylinder is 80 cubic centimeters. if the diameter and height of the cylinder are multiplied by 4/5, what is the volume of the new cylinder?      Log On


   

Question 759158: the volume of a cylinder is 80 cubic centimeters. if the diameter and height of the cylinder are multiplied by 4/5, what is the volume of the new cylinder?
Found 2 solutions by sachi, josgarithmetic:
Answer by sachi(548) About Me  (Show Source):
You can put this solution on YOUR website!
volume of cylinder = pi *r^2*h=80 cc (where r=radius,h=height & d=diameter)
now as given new cylinder wil have
D=4/5d or R=4/5r
& H=4/5h
so the volume = pi*R^2*H=pi*(4/5r)^2*(4/5h)=pi *16/25r^2*4/5h
=pi *r^2*h*(16*4/25*5)=80*64/125=40.96cc

Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Using just symbols, V, D, H, V=H%2Api%2A%28D%2F2%29%5E2.

Now what happens when both of D and H are reduced to 4/5 their value?
v is the volume for dimensions reduced by 4/5.

v=%284%2F5%29H%2Api%2A%28%284%2F5%29D%2F2%29%5E2
v=%284%2F5%29%2AH%2Api%2A%284%2F5%29%5E2%28D%2F2%29%5E2
v=%284%2F5%29%5E3%2AH%2Api%2A%28D%2F2%29%5E2, and in reference to the earlier given formula for V,
highlight%28v=V%2A%284%2F5%29%5E3%29