Intermediate November 2017 Unit 2 Q12
12. A triangular prism of length 2 metres is shown below.
Diagram not drawn to scale
AC = 21 cm, BC = 35 cm and \(B\widehat{A}C\) = 90°.
(a) Calculate the area of triangle ABC.
Give your answer in cm2.
You must show all your working. [5]
Give your answer in cm2.
You must show all your working. [5]
(b) Calculate the volume of the prism.
You must give the units of your answer. [3]
You must give the units of your answer. [3]
From the formula list: Volume of prism = area of cross-section × length
| Scheme | Marks | Comments |
|---|---|---|
| Work for 12(a) must be seen in 12(a) and not awarded retrospectively from work in 12(b). In (a) allow correctly working in metres BUT final answer must be in cm2. | ||
| 352 = 212 + AB2 OR (AB2 =) 352 − 212 | M1 | |
| ( AB2 =) 784 or (AB =) √784 | A1 | F.T. ’their784’ if M1 gained and if <1225 |
| (AB =) 28(cm) | A1 | |
| (Area ABC =) \(\dfrac{21 \times 28}{2}\) | M1 | F.T. (21 × ‘their stated or shown AB’) / 2 AND (AB ≠ 35 and ≠ 21) |
| = 294(cm2) | A1 |
Alternative method.
| Scheme | Marks | Comments |
|---|---|---|
| Cos C = 21/35 | M1 | |
| C = cos−1 0·6 | m1 | |
| ACB = 53(·13..)(°) | A1 | |
| F.T. ‘their 53°’ | ||
| Area ABC = ½ × 21 × 35 × sin 53·13° | M1 | |
| = 294(cm2) | A1 |
Answer from a ‘FT angle’ must be correct to at least 1dp. (Note using 53° leads to 293·498….)
| Scheme | Marks | Comments |
|---|---|---|
| Work for 12(b) must be seen in 12(b). | ||
| Use of ‘Volume = area ABC × length’. | M1 | Allow this M1 even if using ‘mixed units’. Where ‘area ABC’ is that shown in 12(a) or calculated using ‘their AB’ from 12(a) AND the length is ‘2×10n’. (Note: using ‘their AB’ as an area is M0.) |
| (Volume =) 294 × 200 OR 0·0294 × 2 | m1 | F.T. ‘their area of ABC’ OR 294 AND using ‘consistent’ units. |
| = 58800 cm3 OR 0·0588 m3. | A1 | Correct units must be shown. Mark final answer. An unsupported 588 × 10n implies M1. |