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)

Question

m3

Answer 1

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.