Answer: [tex]h = \frac{y}{3}[/tex]
Step-by-step explanation:
The formula for calculating the volume of a cylinder is given as :
[tex]V = \pi r^{2}h[/tex]
The formula for calculating the volume of a cone is given as :
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
Since the cylinder and the cone have the same volume according to the question , we will equate the two formulas, that is:
[tex]\pi r^{2} h=\frac{1}{3}\pi r^{2}h[/tex]
substituting the values of r , we have
[tex]\pi x^{2} y=\frac{1}{3}\pi (3x)^{2}h[/tex]
⇒ [tex]\pi x^{2} y=\frac{1}{3}\pi (9x^{2} )h[/tex]
since [tex]\pi x^{2}[/tex] is common to both sides , it will cancel out , that is
[tex]y = \frac{1}{3}(9)h[/tex]
[tex]3y = 9h[/tex]
divide through by 9
[tex]3y/9 = h[/tex]
Therefore , the height of the cone in terms of y is
[tex]h = \frac{y}{3}[/tex]
