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A scoop of ice cream in the shape of a whole perfect sphere sits in a right cone. The radius of the ice cream scoop is 2.5cm and the radius of the cone is 2.5cm. How tall must the height of the cone be to fit all the ice cream without spilling if it melts?

 Mar 5, 2020
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volume of sphere= 4/3  pi r^3     must equal volume of cone = 1/3  pi r^2 h

 

4/3 pi r^3  =  1/3 pi r^2 h         remove pi r^2 from both sides (r is equal in the ice cream sphere and the cone)

 

4/3 r = 1/3 h       multiply both sides by 3

4r=h

4(2.5) = h = 10 cm

 Mar 5, 2020

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