Final answer:
To find the percentage by which the diameter of the cylinder exceeds its height, we need to compare the diameter and height of the cylinder. Given that the volumes of the sphere and cylinder are equal, we equate their formulas and solve for the height. Then we calculate the percentage difference between the diameter and height.
Step-by-step explanation:
To find the percentage by which the diameter of the cylinder exceeds its height, we need to compare the diameter and height of the cylinder. Let's assume the radius of the sphere and the cylinder is 'r'. We know that the volume of a sphere is given by V = (4/3)πr³ and the volume of a cylinder is given by V = πr²h. Given that the volumes of the two shapes are equal, we can equate their formulas:
(4/3)πr³ = πr²h
Canceling out πr² from both sides, we get:
(4/3)r = h
Now let's compare the diameter and height of the cylinder. The diameter of the cylinder is twice the radius, so it is 2r. Therefore, the percentage by which the diameter exceeds the height is given by:
Percentage = [(2r - h)/h] * 100%