The volume of a sphere is 48m³ what is the volume of a cylinder if it's radius is the same ad the spheres and its height is equal to the spheres diameter
First, let's find the radius of the sphere since the cylinder's radius is the same. The formula to calculate the volume of a sphere is:
V = (4/3)πr³
To find the radius, we rearrange the equation:
r³ = (3V) / (4π)
r³ = (3 * 48m³) / (4π)
r³ = 144m³ / (4π)
r³ = 36m³ / π
r = (36m³ / π)^(1/3)
r ≈ 2.57m
Now, let's find the height of the cylinder since it is the same as the sphere's diameter. The diameter of a sphere is twice the radius:
d = 2r
d = 2 * 2.57m
d ≈ 5.14m
Since the height of the cylinder is equal to the sphere's diameter, the height of the cylinder is approximately 5.14m.
The formula to calculate the volume of a cylinder is:
V = πr²h
Substituting the values we found, we get:
V = π * (2.57m)² * 5.14m
V ≈ π * 6.6049m² * 5.14m
V ≈ 33.5173π m³
Therefore, the volume of the cylinder is approximately 33.5173π m³.