given a cylindrical waterbottle that has a volume of 1.25L, find the radius and a height that is 4-6 times the radius
To find the radius and height of the cylindrical water bottle, we can use the given information about its volume. The formula to calculate the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
Given that the volume of the water bottle is 1.25L, we can equate this to the formula for volume:
1.25 = πr²h
Next, we know that the height (h) is 4-6 times the radius (r):
h = 4r or h = 6r
We can substitute these values into the equation for volume:
1.25 = πr²(4r) or 1.25 = πr²(6r)
Simplifying further:
1.25 = 4πr³ or 1.25 = 6πr³
Now, to solve for the radius, we can isolate it by dividing both sides of the equation by the respective constant:
For h = 4r:
1.25 / (4π) = r³
r = ∛(1.25 / (4π))
For h = 6r:
1.25 / (6π) = r³
r = ∛(1.25 / (6π))
Now, you can calculate the radius using the respective equation and the value of π as 3.14159.
After finding the radius, you can find the corresponding height by substituting the value of r (radius) into the equation h = 4r or h = 6r.