Higher June 2019 Unit 2 Q20
20. Two similar solids have base areas of 47 cm2 and 199 cm2, as shown below.
The volume of the smaller solid is 350 cm3.
Diagram not drawn to scale
Calculate the volume of the larger solid. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Volume scale factor: \(\left(\sqrt{199/47}\right)^3\) (=8.712…) OR \(\left(\sqrt{47/199}\right)^3\) (=0.114…) or equivalent. | B2 | May be seen in parts. Award B1 for a linear scale factor: \(\sqrt{(199/47)}\) (= 2.057…) OR \(\sqrt{(47/199)}\) (= 0.485…) or equivalent OR Award B1 for (199/47)3 (= 75.904…) OR (47/199)3 (= 0.013...). |
| Volume of larger solid \(350 \times \left(\sqrt{199/47}\right)^3\) OR \(350 \div \left(\sqrt{47/199}\right)^3\) or equivalent. | M1 | |
| 3049(.305…cm3) | A1 | CAO. Not from premature approximation. |