Higher June 2017 Paper 6 Q8

OCRHigherCurrent spec5 marksCompound Measures

8 The object below is made from a square-based pyramid joined to a cuboid.

A square-based pyramid on top of a cuboid; the cuboid has base side 4 cm and height 8 cm, and the total height of the object is 13 cm

The base of the cuboid and the base of the pyramid are both squares of side 4 cm.
The height of the cuboid is 8 cm and the total height of the object is 13 cm.
The total mass of the object is 158 g.

The cuboid is made from wood with density 0.67 g/cm\(^3\).
The pyramid is made from granite.

Calculate the density of the granite.

[The volume of a pyramid is \(\frac{1}{3}\) × area of base × perpendicular height.] [5]

Mark scheme

Answer	Marks	Part marks and guidance
2.7 nfww	5	Allow 2.70 to 2.71	Condone for full marks minor inaccuracies from rounding if final answer given as 2.7
		M2 for 4 × 4 × 8 × 0.67 or M1 for 4 × 4 × 8	= 85.76 (mass of cuboid) = 128 (vol of cuboid)
		AND
		M1 for \(\frac{1}{3} \times 4 \times 4 \times (13 - 8)\)	= 26.6 to 26.7 (vol of pyramid)
		AND
		M1 for their 85.76 + their 26.7\(x\) = 158 oe	eg (\(x =\)) \(\dfrac{158 - \mathit{their}\,85.76}{\mathit{their}\,26.7}\)