4. PressiePacs is a company that designs and makes presentation boxes.
(a)
Two designs, small and large, are shown below. PressiePacs wants the large box to have twice the volume of the small box.
Diagrams not drawn to scale
Calculate the height of the large box. [5]
(b)
Customers can use this formula to calculate the cost of a presentation box:
Cost in £ = Surface area of the box in cm2 ÷ 240
Calculate the cost of the small presentation box. [3]
Cost of the small presentation box is £ ……………
Mark scheme (a)
Scheme
Marks
Comments
(Volume of the small box) 10 × 10 × 10 or (Volume of the large box) 2 × 10 × 10 × 10
M1
(Volume of the small box) 1000 (cm3) or (Volume of the large box) 2000 (cm3)
A1
May be implied in further working
Height of large box × 12.5 × 12.5 = 2 × 1000 or Height of large box × 12.5 × 12.5 = 2000
m1
FT incorrect evaluation of volume Allow for evidence of trial to find the height such that a clear attempt to get an answer of approximately 2000 provided 2000 seen, e.g. volume 2000 (cm3) followed by 13 × 12.5 × 12.5 = 2031.25. Not for sight of 12.5 × 12.5 × 12.5 (= 1953.125)
(Height of large box =) \(\dfrac{2 \times 1000}{12.5 \times 12.5}\) or equivalent
M1
FT from previous M1 m0, for omitted 2 or incorrect interpretation of ‘twice’ provided appropriate rearrangement is in the form \(\dfrac{10 \times 10 \times 10}{12.5 \times 12.5}\) or \(\dfrac{10 \times 10 \times 10}{2 \times 12.5 \times 12.5}\) or equivalent i.e. must include (10 × 10 × 10) ÷ (12.5 × 12.5) with incorrect interpretation of ‘2’ or omitted ‘2’
(2000 ÷ 156.25 =) 12.8 (cm)
A1
CAO Allow final M1 A1 for an embedded correct answer if not contradicted, e.g. 12.5 × 12.5 × 12.8 = 2000
Mark scheme (b)
Scheme
Marks
Comments
(Surface area of the box) 6 × 10 × 10 (= 600)
B1
(Cost) 6 × 10 × 10 ÷ 240
M1
FT ‘their surface area’ provided it is a multiple of 100 and 300 ≤ ‘their surface area’ ≤ 600, i.e. only FT 300, 400 and 500
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