Answer: 3 : 1
Step-by-step explanation:
The formula for finding the volume of a cone is given by :
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
While the formula for calculating the volume of a cylinder is given by :
[tex]V = \pi r^{2}h[/tex]
Since the two volumes are equal according to the question , then we have :
[tex]\frac{1}{3}\pi r^{2}h = \pi r^{2}h[/tex]
Also , since they have the same radius and [tex]\pi[/tex] is common to the two , we will be left with :
[tex]\frac{1}{3}h_{a}[/tex] = [tex]h_{b}[/tex]
That is
[tex]h_{a} = 3h_{b}[/tex]
Therefore , the ratio of the height of cone A to the height of cylinder B = 3 : 1
