Higher November 2017 Paper 3 Q27

VABCD is a square-based pyramid.

The horizontal base ABCD has side length 10 cm and centre M.

Angle VMA is 90°

Angle VAM is 68°

Volume of pyramid \(= \dfrac{1}{3} \times\) area of base \(\times\) perpendicular height

Work out the volume of the pyramid. [6 marks]

Mark scheme

Answer	Mark	Comments
\(10^2 + 10^2\) or 200 or \(5^2 + 5^2\) or 50	M1	oe
\(\sqrt{\text{their } 200}\) or \(10\sqrt{2}\) or [14, 14.2] or \(\sqrt{\text{their } 50}\) or \(5\sqrt{2}\) or [7, 7.1]	M1dep	oe
\(\tan 68 = \dfrac{h}{\text{their } 7.1}\)	M1dep
their \(7.1 \times \tan 68\) or [17.3, 17.6]	M1dep
\(\dfrac{1}{3} \times 10 \times 10 \times\) their [17.3, 17.6]	M1dep
[576, 587] or 590	A1