An ancient civilisation buried its kings and queens in tombs in the shape of a square-based pyramid,
The kings and queens were each buried in a pyramid with
Each of the isosceles triangle faces is congruent to each of the other triangular faces.
The base angle of each of these triangles is
Pyramid
- i. Find
in terms of . (1 mark)
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- ii. Find
in terms of . (1 mark)
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- Show that the total surface area (including the base),
, of the pyramid, , is given by -
. (2 marks)
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- Find
, the height of the pyramid , in terms of . (2 marks)
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- The volume of any pyramid is given by the formula
. - Show that the volume,
, of the pyramid is . (1 mark)
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Queen Hepzabah’s pyramid was designed so that it had the maximum possible volume.
- Find
and hence find the exact volume of Queen Hepzabah’s pyramid and the corresponding value of . (4 marks)
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Queen Hepzabah’s daughter, Queen Jepzibah, was also buried in a pyramid. It also had
The volume of Jepzibah’s pyramid is exactly one half of the volume of Queen Hepzabah’s pyramid. The volume of Queen Jepzibah’s pyramid is also given by the formula for
- Find the possible values of
, for Jepzibah’s pyramid, correct to two decimal places. (2 marks)
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