A scoop of ice cream, shaped like a sphere with a diameter of 6 cm, is placed in an ice cream cone with diameter 5 cm and height 12 cm. Is the cone big enough to hold all the ice cream if it melts? Explain.

Question

anonymous · Answer

to hold

anonymous · Answer

Look up the volume formulas or derive them by integration. You'll get:

Volume of cone is pi r(cone)^2 h(cone)/3 = pi (2.5)^2 12/3 = 25 pi (cm^3)

Volume of ice cream sphere is (4/3)pi r(sphere)^3 = (4/3)*pi*3^3 = 36 pi (cm^3).

Volume of ice cream is larger than that of cone so the cone is not large enough to hold the ice cream.

This answer assumes the volume of the ice cream is the same frozen or melted. However ice cream always contains some air, so when melted, the volume will be less.  Not enough info (like how much air is present in the ice cream in its frozen state) is given to solve if you drop that assumption.