4MA0 Higher June 2015 Paper 3 Q11
11 Here is a prism.
Diagram NOT accurately drawn
\(ABCDEF\) is a cross section of the prism.
\(ABCF\) is a square of side 12 cm.
\(FCDE\) is a trapezium.
\(ED = 22\) cm.
The height of the prism is 20 cm.
The length of the prism is 80 cm.
Work out the total volume of the prism.
(5)
NB: If it is clear that the surface area is being calculated then no marks can be awarded
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{2} \times (12 + 22) \times (20 - 12)\) oe (= 136) | M1 |
| 12 × 12 (= 144) | M1 |
| “136” + “144” = 280 | M1 |
| 80 × “280” | M1 |
| 22400 | A1 |
| (5) |
Notes
M1: dep on at least one previous M1 scored
M1: dep on previous M1
Alternative
| Scheme | Marks |
|---|---|
| \(\dfrac{1}{2} \times (12 + 22) \times (20 - 12)\) oe (= 136) | M1 |
| 12 × 12 (= 144) | M1 |
| “136” × 80 = 10880 or “144” × 80 = 11520 | M1 |
| “10880” + “11520” | M1 |
| 22400 | A1 |
Notes
M1: (may be seen within a volume calculation)
M1: (may be seen within a volume calculation)
M1: dep on at least one previous M1 scored
M1: dep on previous M1
Special Case: Use of 10cm for height of trapezium AND 10cm for \(AF\)
B3 for answer of 23200
If not B3 then B2 for 290 × 80 or \(80 \times \left(10 \times 12 + \dfrac{1}{2} \times (22 + 12) \times 10\right)\)
If not B2 then B1 for \(10 \times 12 + \dfrac{1}{2} \times (22 + 12) \times 10\) (= 290) or 10 × 12 × 80 and \(\dfrac{1}{2} \times (22 + 12) \times 10 \times 80\)