A cylinder whose volume is 386,000m3 has it's length 1.3 times its diameter. calculate the diameter of the cylinder given that the volume V = 3.142r2h.
v = πr^2 h
Just plug in the known values
386000 = π r^2 (1.3*2r) = 2.6π r^3
r^3 = 386000 / 2.6π
r = 36.15, so
d = 72.30
To calculate the diameter of the cylinder, we need to use the given volume equation and the relationship between the length and diameter of the cylinder.
Let's start by breaking down the information given:
- The volume, V, of the cylinder is 386,000 m^3.
- The length of the cylinder, h, is 1.3 times its diameter, which can be written as h = 1.3d, where d is the diameter of the cylinder.
Now we can substitute these values into the volume equation: V = 3.142r^2h.
Replacing h with 1.3d, we have:
386,000 = 3.142r^2(1.3d).
Next, we simplify the equation:
386,000 = 4.0854(3.142d^3).
386,000 = 12.8727d^3.
Now, divide both sides of the equation by 12.8727 to isolate d^3:
d^3 = 29,976.9.
To find the value of d, we need to find the cube root of 29,976.9, which can be done using a calculator:
d ≈ cube root of (29,976.9) ≈ 31.6.
Therefore, the diameter of the cylinder is approximately 31.6 meters.