The volume of a sphere is 48 m3 . 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)
m3
Let's start with the volume of a sphere formula:
V_sphere = (4/3) * π * r^3
Given that the volume of the sphere is 48 m^3, we can set up the equation:
48 = (4/3) * π * r^3
Next, let's find the radius (r) of the sphere. We can rearrange the equation:
48 = (4/3) * π * r^3
48 / ((4/3) * π) = r^3
12 / π = r^3
Taking the cube root of both sides:
r = (12 / π)^(1/3)
Now, let's find the diameter (d) of the sphere, which is twice the radius:
d = 2 * r
Next, we are given that the height of the cylinder is equal to the sphere's diameter, so the height (h) of the cylinder is also d:
h = d = 2 * r
Finally, let's find the volume (V_cylinder) of the cylinder using the formula:
V_cylinder = π * r^2 * h
V_cylinder = π * r^2 * (2 * r)
V_cylinder = 2πr^3
Substituting the value for r:
V_cylinder = 2π * ((12 / π)^(1/3))^3
V_cylinder = 2π * (12 / π)
V_cylinder = 24
Therefore, the volume of the cylinder is 24 m^3.