The diagram shows a right pyramid with a rectangular base WXYZ and vertex O. If |WX| = 8 cm, |ZW| = 6 cm and |OX| = 13 cm, calculate the:
height of the pyramid;
value of ∠OXZ, correct to the nearest degree;
volume of the pyramid.
Observation
The Chief Examiner reported that while majority of those who attempted this question were able to find the height of the pyramid, some of them could neither calculate the value of ∠OXZ nor the volume of the pyramid correctly. They were reported to have quoted the formula for finding the volume of the pyramid wrongly. Candidates were expected to find |XM| by first finding |ZX| and dividing the answer by 2. Using the Pythagoras theorem, |ZX|2 = |ZW|2 + |WX|2 =
82 + 62 = 100. Therefore, |XM| = = = 5 cm. The height of the pyramid, |OM| = = = 12 cm. Candidates were also expected to show that if ∠OXZ = y, then cos y = = . Hence, ∠OXZ = cos-1() = 67o.
Volume of pyramid = × base area × height = × 8 × 6 × 12 = 192 cm3.
= 
= 5 cm. The height of the pyramid, |OM| = 
= 
= 12 cm. Candidates were also expected to show that if ∠OXZ = y, then cos y = 
= 
. Hence, ∠OXZ = cos-1(
) = 67o.
× base area × height = 
× 8 × 6 × 12 = 192 cm3.