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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?

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2 Answers

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 Vcylinder = ∏(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

 

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You're welcome! Glad it was helpful

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Vcone = (1/3)(pi)r2cone hcone    
Vcylinder = (pi)r2cylinder hcylinder   

Vcyl. = (pi)*36*18 = (pi)*648
Vcone = (1/3)(pi)*81*hcone = (pi)*648
(pi)*27*hcone = (pi)*648
hcone = (pi)*648 / (pi)*27    
hcone = 24 cm