Higher June 2022 Paper 3 Q16
16 Here is a scale drawing of a reservoir.
Scale: 1 cm represents 500 m
Virat wants to estimate the volume of water in the reservoir.
He draws on the scale drawing a circle with radius 3 cm
(a) Virat estimates the volume of the reservoir by assuming that
- the reservoir is a cylinder whose cross section is the circle
- the depth of the reservoir is 17 metres.
Work out Virat’s estimate in cubic metres. [3 marks]
(b) In fact,
- the depth of the reservoir is 13.8 metres
- the reservoir is not a cylinder (see diagram).
Which statement about the actual volume of the reservoir is correct?
Tick one box.
- It is less than Virat’s estimate
- It is greater than Virat’s estimate
- It could be less than or greater than Virat’s estimate
Give a reason for your answer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(3 \times 500\) or 1500 | M1 | actual radius of circle in metres |
| (their \(1500)^2 \times \pi \times 17\) or \(38\,250\,000\pi\) | M1dep | |
| [120 000 000, 120 200 000] or [\(1.2 \times 10^8\), \(1.202 \times 10^8\)] | A1 | accept in words eg 120 million SC1 [480, 481] or [0.048, 0.0481] |
Additional guidance
Do not award A mark if incorrect further work is seen
| Answer | Mark | Comments |
|---|---|---|
| It could be less than or greater than Virat’s estimate (3rd box ticked) and statement that area is larger but depth is smaller | B2 | B1 It is less than Virat’s estimate (1st box ticked) and statement that depth is smaller or It is greater than Virat’s estimate (2nd box ticked) and statement that area is larger or It could be less than or greater than Virat’s estimate (3rd box ticked) and statement that depth is smaller or It could be less than or greater than Virat’s estimate (3rd box ticked) and statement that area is larger |
Additional guidance
| For B2 their statement must refer to larger area and smaller depth | |
| For B1 their statement must correctly refer to larger area or smaller depth for their box ticked | |
| Examples of statements implying actual depth is smaller: height is less depth is lower it is shallower Virat’s estimate of the depth is bigger | |
| Examples of statements implying actual area is larger: the width is bigger cross section is bigger shape is greater Virat’s estimate of the area is smaller | |
| The reservoir could be bigger or smaller | B0 |
| The reservoir is larger | B0 |
| We do not know the depth | B0 |