Intermediate November 2023 Unit 2 Q14
14.
Diagram not drawn to scale
(a) Find the volume of the solid prism shown above. [3]
(b) The solid prism is made of gold.
Gold has a density of 19·3 g/cm3.
Calculate the mass of the prism.
Give your answer in kilograms. [3]
Gold has a density of 19·3 g/cm3.
Calculate the mass of the prism.
Give your answer in kilograms. [3]
Mass of the prism = …………… kg
From the formula list: Area of trapezium \(= \dfrac{1}{2}(a+b)h\); Volume of prism = area of cross-section × length
| Scheme | Marks | Comments |
|---|---|---|
| (Area =) \(\dfrac{7{\cdot}4 + 9{\cdot}1}{2} \times 5{\cdot}7\) or equivalent | M1 | (= 47·025) May be seen in stages. Allow M1 for correct intent seen. e.g. 7·4 + 9·1 × 5·7 ÷ 2 |
| × 15·6 | m1 | |
| Allow an answer from 733 to 734 (cm3) inclusive. | A1 | CAO Note: 733·59 or 733·6 (cm3) |
| Scheme | Marks | Comments |
|---|---|---|
| 733·59 × 19·3 | M1 | FT ‘their volume from (a)’ × 19·3 |
| 14158(·287 (g)) | A1 | |
| Allow an answer from 14·1 to 14·2 (kg) inclusive. | B1 | FT ‘their 14158·287’ ÷ 1000 Allow 14 from correct working. Note: 14·158(287) or 14·16 or 14·2 (kg) |
14.(b) Alternative method (converting to g first)
| Scheme | Marks | Comments |
|---|---|---|
| 0·0193 (kg/cm3) | B1 | |
| 733·59 × 0·0193 | M1 | FT ‘their volume from (a)’ and FT ‘their 0.0193’ provided a place value error has been made. |
| Allow an answer from 14·1 to 14·2 (kg) inclusive | A1 | Allow 14 from correct working. Note: 14·158(287) or 14·16 or 14·2 (kg) |