(a) Draw an accurate plan view of the prism on the one-centimetre square grid below.
[3]
(b) Show that the volume of the prism is 72 cm\(^3\). [2]
(c) A cuboid with a square base also has a volume of 72 cm\(^3\). The height of the cuboid is 2 cm. Work out the length of one side of the square base. [3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Rectangle 8 by 6 with one internal line 2 cm from longer edge
3
B1 for a rectangular base
B1 for 8 by 6 or for any rectangle with one line drawn inside parallel to longer edge
Accept in any orientation
e.g. 8 by 6 scores B1B1 8 by 6 with wrong line scores B1B1 8 by 5 scores B1B0 8 by 5 with one line scores B1B1
Mark scheme (b)
Answer
Marks
Part marks and guidance
\(6 \times 3 \times 8 \div 2\) [\(= 72\)]
M2
M1 for \(6 \times 3 \div 2\) oe or for their area or cross section \(\times 8\)
May be done in stages
Mark scheme (c)
Answer
Marks
Part marks and guidance
6
3
M2 for \(\sqrt{\dfrac{72}{2}}\) oe or M1 for \(l \times l \times 2 = 72\) oe or for \(72 \div 2\)
