Recasting a metal cone and comparing surface areas
Recasting a metal cone and comparing surface areas
IP 2
8 marks
A solid metal cone has base radius \(6\) cm and height \(8\) cm. It is melted and recast without loss of metal.
- The metal is recast into a solid cylinder of radius \(4\) cm. Find the height of the cylinder.[2]
- Find the total surface areas of the cone and of the cylinder in terms of \(\pi\), and the percentage decrease in surface area.[3]
- Instead, the metal is recast into a single solid sphere. Find its surface area, and state which of the three shapes has the least surface area for the same volume.[3]
Solution:
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Answer:(a) \(6\) cm (b) Cone \(96\pi\text{ cm}^2\), cylinder \(80\pi\text{ cm}^2\); \(16.7\%\) decrease (c) \(69.2\pi\text{ cm}^2\); the sphere
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