A cylinder of radius 6 cm and height 18 cm is full of water. What must be the height of a cone with radius 9cm to hold the same amount of water?

Question

dont know how to do

Answer 1

Since the question asks about how much water something can hold that should let you know we need to use volume.

The volume of a cylinder is ∏r²h and the volume of a cone is (1/3)∏r²h where r represents radius and h represents height.

First we find the volume of the cylinder V_cylinder = ∏(6)²(18)= 648∏.

Our goal is to find the height of the cone which gives us the same volume. To do this we set the volume of the cylinder we just found equal to the volume of the cone and simply solve for h.

Hope this was helpful, let me know if you want me to elaborate more

 

Answer 2

V_cone = (1/3)(pi)r²_cone h_cone    
V_cylinder = (pi)r²_cylinder h_cylinder   

V_cyl. = (pi)*36*18 = (pi)*648
V_cone = (1/3)(pi)*81*h_cone = (pi)*648
(pi)*27*h_cone = (pi)*648
h_cone = (pi)*648 / (pi)*27    
h_cone = 24 cm