The volume of a sphere is given by the formula:
V_sphere = (4/3)πr^3
where r is the radius of the sphere.
Since the volume of the sphere is 48 m^3, we can set up the equation:
48 = (4/3)πr^3
To find the radius, we can solve this equation for r:
r^3 = (3/4) * (48/π)
r^3 ≈ 18.85
Taking the cube root of both sides, we find:
r ≈ 2.74
Now, let's find the diameter of the sphere. The diameter is twice the radius:
d = 2r ≈ 5.48
The height of the cylinder is equal to the sphere's diameter, so h = d ≈ 5.48.
The volume of a cylinder is given by the formula:
V_cylinder = πr^2h
Substituting the values we found:
V_cylinder = π * (2.74)^2 * 5.48
Simplifying, we find:
V_cylinder ≈ 214.07 m^3
Therefore, the volume of the cylinder is approximately 214.07 cubic meters.
the volume of a sphere is 48 m^3. 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
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