Prisms: WJEC GCSE Numeracy Intermediate November 2018 Unit 2 Q9

Numeracy Intermediate November 2018 Unit 2 Q9

WJECIntermediateCurrent spec6 marksPrisms Pythagoras

(a) Luned’s tent is in the shape of a triangular prism.
The cross-section of her tent is an isosceles triangle.

She noted a few measurements on a diagram of her tent, as shown below.

Tent shaped as a triangular prism: length 2·5 m, sloping side 1·8 m, half the base width 0·7 m, with the perpendicular height marked

Diagram not drawn to scale

Calculate the volume of Luned’s tent.
Give your answer in m³.
You must show all your working. [5]

From the formula list: Volume of prism = area of cross-section × length

Volume of Luned’s tent is …………… m³

(b) Which of the following is equal to 0·2 m³?
Circle your answer. [1]

20 cm³ 200 cm³ 2000 cm³ 200 000 cm³ 2 000 000 cm³

Mark scheme (a)

Scheme	Marks	Comments
(Perpendicular height, h) (h² =) 1.8² – 0.7² or 1.8² = h² + 0.7²	M1
h² = 2.75 or (h =) √2.75	A1	Accept √11 ⁄ 2
(Perpendicular height is) h = 1.658(...m) or 1.66 (m) or 1.7 (m)	A1	Accept √11 ⁄ 2 Do not accept truncation to 1.6(m) or 1.65 (m) (But FT allowed) FT from M1, A0 for the correctly evaluated square root of ‘their 2.75’ provided ‘their answer’ <1.8 (m)
(Volume of Luned’s tent =) ½ × (0.7+0.7) × 1.658.... × 2.5 or equivalent	M1	FT ‘their derived 1.658(....)’ provided ≠1.8 or ≠0.7
(Volume) Answer in the inclusive range 2.9 (m³) to 2.98(m³) or 3(.0m³)	A1	Check from correct working (in particular for an answer of 3(m³)) FT 1.6m or 1.65m to an answer in the range 2.8(m³) to 2.89(m³) FT from previous M1 awarded for a similar range