Final answer:
To find the volume of the sphere, you need to first determine the radius of the cylinder using its volume formula. Then, you can use the volume formula for a sphere to calculate the volume with the given radius.
Step-by-step explanation:
To find the volume of a sphere with the same radius as the given cylinder and a height equal to the sphere's diameter, we can use the relationship between the formulas for the volumes of a sphere and a cylinder. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. In this case, the volume of the cylinder is 36 cm³. Therefore, we can rearrange the formula to solve for the radius: r = √(V / πh) = √(36 / (3.142 × 5.25)) ≈ 0.750 cm. Now, we can use the formula for the volume of a sphere, which is V = (4/3)πr³, to find the volume of the sphere. Substituting the radius we found, we get V = (4/3)π(0.750)³ = 4.712 cm³.