Square pyramid recast into unequal spheres

Square pyramid recast into unequal spheres

Secondary 2
8 marks
TGM Original Questions

Core stretch

A right square pyramid has base side 10 cm and height 24 cm.

  1. Find its base diagonal.[2]
  2. Find a slant edge from vertex to base corner.[2]
  3. Find its volume.[2]
  4. It is melted into two spheres whose radii are \(r\) and \(2r\). Using \(\pi=3.142\), find \(r\) to 3 significant figures.[2]

Solution:

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Answer:(a) \(10\sqrt2\) cm (b) \(\sqrt{626}\approx25.0\) cm (c) \(800\text{ cm}^3\) (d) \(2.77\) cm.

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