Simplify the following paragraph: To find the volume of a cylinder with the same radius as a sphere and a height equal to the sphere's diameter, we need to first determine the sphere's radius.
The volume formula for a sphere is given by V = (4/3) * π * r³, where V is the volume and r is the radius.
In this case, we are given that the volume of the sphere is 48 m³, so we can rewrite the equation as 48 = (4/3) * π * r³.
Solving this equation for r³, we get r³ = (48 * 3) / (4 * π) = 36 / π.
Next, we need to find the diameter of the sphere. The diameter is twice the radius, so the diameter = 2 * r.
Given that the height of the cylinder is equal to the sphere's diameter, the height of the cylinder is equal to 2 * r.
Now, we can calculate the volume of the cylinder using the formula V = π * r² * h, where V is the volume, r is the radius, and h is the height.
Substituting the values, we have V = π * r² * (2 * r) = 2 * π * r³.
Plugging in the value we found for r³ earlier, we have V = 2 * π * (36 / π) = 72.
Therefore, the correct answer is 72 m³, not 226.195 m³. The value of 226.195 m³ does not represent the volume of the cylinder in this context.