Suppose that a sphere with radius 5a has the same volume as a cone of radius 3a. What is the height of the cone? Give your answer in terms of a. Use the formulas (Posted below) for the volume of a sphere and cone respectively.

Question

anonymous · Answer

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anonymous · Answer

take ratio i.e divide thees formulas and find a relation in terms of "h", sub radius of sphere =3a and same as radius of cone

OR 

Just equate the volumes, put r=3a and find value of 'h'

anonymous · Answer

can you show me how to do that

anonymous · Answer

they have same volumes so

$$\frac{ 4 }{ 3 }\pi r ^{3}=\frac{ 1 }{ 3 }pi r ^{2}h$$

anonymous · Answer

Do you understand what is going on with this problem yet?

anonymous · Answer

cancel pi and 3, and put r=3a for cone and r= 5a for sphere
solve for h