The volume of a sphere is 18 Divided by
5π cm3. What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Let's call the radius of the sphere and the cylinder r.
We are given that the volume of the sphere is 18/(5π) cm^3.
So, (4/3)πr^3 = 18/(5π)
Multiplying both sides by (5π) gives us:
(4/3)πr^3 * (5π) = 18
Simplifying the expression on the left side:
(4/3) * 5 * r^3 * π * π = 18
(20/3)π^2 * r^3 = 18
Dividing both sides by (20/3)π^2 gives us:
r^3 = 18 / ((20/3)π^2)
r^3 = (54/20) / π^2
r^3 = (27/10) / π^2
r^3 = 27 / (10π^2)
Taking the cube root of both sides:
r = ∛(27 / (10π^2))
Now, the height of the cylinder is equal to the sphere's diameter, which is 2r:
height = 2 * r = 2 * ∛(27 / (10π^2))
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
So, the volume of the cylinder is:
V = π * r^2 * height
V = π * (∛(27 / (10π^2)))^2 * (2 * ∛(27 / (10π^2)))
Simplifying this expression would be difficult because of the cube roots and irrational numbers involved. However, you can calculate an approximate value for the volume using a calculator.