A melting scoop of ice cream on a cone
A melting scoop of ice cream on a cone
IP 2
8 marks
An empty ice-cream cone is a hollow right circular cone, vertex down, with rim radius \(3\) cm and depth \(10\) cm. A hemispherical scoop of ice cream of radius \(3\) cm rests on the rim with its flat face exactly covering the opening.
- Find, in terms of \(\pi\), the volume of the scoop and the capacity of the cone.[2]
- The scoop melts and all of it runs into the cone. Show that it does not overflow, and find the depth of the melted ice cream in the cone.[4]
- State one assumption in (b) and explain how the real depth may differ.[2]
Solution:
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Answer:(a) \(18\pi\text{ cm}^3\), \(30\pi\text{ cm}^3\) (b) \(18\pi<30\pi\); depth \(8.43\) cm (c) Volume unchanged on melting; real ice cream contains air, so the depth would be less
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