find cylinder volume?

Question

If I have a cyclinder with a diameter of 2.75", what would a proportional cylinders' diameter be if it could hold 8 times the volume? Please explain mathmaticaly....thanks

Answer 1

New diameter = 5.5"

If you have a solid of volume V, and increase it proportionally so that some linear measurement (such as the diameter or height) increases from d to a*d, the volume will increase by a^3*d. Since the volume increases by a factor of 8, each linear measurement will increase by a factor of the cube root of 8, which is 2. Thus the new diameter is 2*2.75" = 5.5".

Answer 2

Volume of a cylinder (V) = Length (L) * pi * radius (r)^2

V= L * pi * r^2
V= L * pi * (1.375^2)
V= L * pi * (1.890625)

Now, multiply each side by 8, o get 8 times the volume (NOTE: This is assuming that the Length of the cylinder DOES NOT change.)

8V= L * pi * (1.890625) (8)
8V= L * pi * (15.125)

Get the square root of 15.125 to get the radius, and then multiply that number by 2 to get the new diameter

square root of 15.125 = 3.889

Diameter = 7.778"

Answer 3

pi (d/2)^2 h = V (8)

d^2/4 = 8V/ pi h

d = sqrt 32V / pi h

Since neither your volume or height are limited you have an infinite number of possibilities for the diameter, only as long as the above equation is satisfied.

Answer 4

it should have a diameter of 5.5" as the volume is proportional to the cube of the radius/diameter

Answer 5

Volume = π x r x r x h
.... Let h = 1
3.142 x 1.375 x 1.375 x 1 = 5.940 x 1
New volume = 8 x 5.940 = 47.523in³
√47.523 ÷ 3.142 = 3.9" radius x 2 = 7.8" diameter.

Answer 6

To calculate volume you need the height of the cylinder