Percentages: WJEC GCSE Numeracy Higher June 2022 Unit 1 Q7

Numeracy Higher June 2022 Unit 1 Q7

WJECHigherCurrent spec6 marksPercentages Volume & Surface Area

7. Tregareth Zoo has a large glass enclosure for reptiles.
The enclosure consists of a hollow rectangular-based pyramid sitting on top of a cuboid, as shown below.

Enclosure: a rectangular-based pyramid sitting on top of a cuboid

Diagram not drawn to scale

The enclosure is to be modified by placing a wooden cuboid onto the base.
This cuboid will reduce the capacity of the enclosure.

Enclosure with a wooden cuboid on its base; the cuboid part is 5 m by 8 m by 3 m high. Front view shows the 8 m wide, 3 m high cuboid with the pyramid of height 1.5 m on top and the wooden cuboid on the floor

Diagrams not drawn to scale

The pyramid has a vertical height of 1·5 m.
The inserted wooden cuboid has dimensions 4 m by 3·5 m by 0·5 m.

Calculate the capacity of this modified enclosure as a percentage of the capacity of the original enclosure. [6]

Capacity of modified enclosure is …………………… % of the capacity of original enclosure

Mark scheme

Scheme	Marks	Comments
(Capacity of original enclosure =) 5 × 8 × 3 + \(\dfrac{1}{3}\) × 5 × 8 × 1.5 (120) (20)	M2	M1 for 5 × 8 × 3 + n × 5 × 8 × 1.5 where 0 < n < 1
= 140 (m³)	A1	CAO
(Volume of wooden cuboid = 4 × 3.5 × 0.5 =) 7 (m³)	B1	May be implied by ‘their original capacity’ – 7
(Percentage =) \(\dfrac{140 - 7}{140}\) (× 100) OR 100 – \(\dfrac{7}{140}\) × 100	M1	FT ‘their derived 140’ and ‘their 4 × 3.5 × 0.5’
= 95 (%)	A1	On FT, their answer needs to be correctly calculated with any slips only being allowed in the decimal part of the percentage, provided it would round to the appropriate whole number. If their division not seen, their rounded answer needs to be correct for their division.