To find the volume of the cylinder, we first need to calculate the radius and height of the cylinder.
Given that the volume of the sphere is 48 m³, the formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.
Given that the volume of the sphere is 48 m³, we have:
48 = (4/3)πr³
r³ = (3/4) * 48 / π
r = ∛(36 / π)
Now, the height of the cylinder is equal to the diameter of the sphere, which is twice the radius of the sphere. So, the height of the cylinder is 2r.
The volume of the cylinder is given by the formula V_cylinder = πr²h, where r is the radius and h is the height.
Substitute the values of r and h into the formula:
V_cylinder = π(∛(36 / π))²(2∛(36 / π))
V_cylinder = π(36 / π)(4 / π)
V_cylinder = 144 / π
Therefore, the volume of the cylinder is approximately 45.80 m³.
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)
1 answer