4MA0 Higher June 2015 Paper 4 Q14
14 \(L\) and \(M\) are two mathematically similar prisms.
Diagram NOT accurately drawn
Prism \(L\) has length 8 cm.
Prism \(M\) has length 20 cm.
Prism \(L\) has height 3 cm.
(a) Work out the height of prism \(M\). (2)
Prism \(M\) has a volume of 1875 cm3
(b) Work out the volume of prism \(L\). (2)
| Scheme | Marks |
|---|---|
| \(\dfrac{20}{8} \times 3\) oe | M1 |
| 7.5 | A1 |
| (2) |
Notes
A1: oe
| Scheme | Marks |
|---|---|
| \(1875 \div \left(\dfrac{20}{8}\right)^3\) oe | M1 |
| 120 | A1 |
| (2) |
Notes
M1: for \(\left(\dfrac{20}{8}\right)^3\) or \(\left(\dfrac{8}{20}\right)^3\) oe, accept ratios
Alternative
| Scheme | Marks |
|---|---|
| \(\dfrac{1875}{20} \times \left(\dfrac{8}{20}\right)^2\) (= 15) oe | M1 |
| 120 | A1 |