Numeracy Intermediate June 2017 Unit 2 Q14
14. Elin’s old fish tank is leaking.
Diagram not drawn to scale
This old fish tank is in the shape of a cuboid.
The base of this tank measures 60 cm by 40 cm.
Before the leak, the height of the water level in Elin’s old fish tank was 45 cm.
Elin decides to replace her fish tank with a cylindrical one.
Diagram not drawn to scale
She selects a new cylindrical fish tank that has a radius of 25 cm and a height of 70 cm.
Will all the original contents, including the water and the fish, fit into this cylindrical tank?
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Old fish tank contains) 60 × 40 × 45 | B1 | (108 000 cm3) |
| (New fish tank maximum volume is) π × 252 × 70 | M1 | |
| Answer in range 137375 to 137500 (cm3) | A1 | |
| Conclusion, e.g. ‘137 375 > 108 000’, ‘Elin can be certain as the volume of the new tank is greater’ ‘it fits’ | B1 | FT ‘their new fish tank calculation’ conclusion provided 108 000 (cm3) seen and at least M1 previously awarded Alternative: (To find new fish tank water level) (Old fish tank contains) 60 × 40 × 45 B1 (New tank) π × 252 × ‘water level’ M1 60×40×45 = π×252בwater level’ m1 (Water level) 55.(.…cm) with conclusion that contents will be certain to fit (55 cm must be correct) A1 Depends on all previous marks awarded |
Corrected by Westie's Workshop
- The board's mark scheme printed “137375 to137500”. Changed to “137375 to 137500” because a space is missing between “to” and the number.
Original: see the board's mark scheme PDF (link above).