Higher June 2024 Paper 3 Q7
7 A paddling pool is in the shape of a cylinder.
The pool has radius 100 cm.
The pool has depth 30 cm.
The pool is empty.
It is then filled with water at a rate of 250 cm3 per second.
Work out the number of minutes it takes to fill the pool completely.
Give your answer correct to the nearest minute.
You must show all your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 63 | P1 | for process to find volume, eg \(\pi \times 100^2 \times 30\ (= 300\,000\pi\) or \(942\,477(.796...))\) |
| P1 | for process to find time in seconds, eg \(\text{``}942\,477(.796...)\text{''} \div 250\ (= 1200\pi\) or \(3769(.911...))\) or \([\text{volume}] \div 250\) or for converting rate to minutes, eg \(250 \times 60\ (= 15\,000)\) | |
| P1 | for complete process eg \(\text{``}3769(.911...)\text{''} \div 60\ (= 20\pi)\) or \(\text{``}942\,477(.796...)\text{''} \div \text{``}15\,000\text{''}\ (= 20\pi)\) | |
| A1 | for answer in the range 62 to 63 |
Additional guidance
(volume =) 942 478 implies P1
(time =) 3770 implies P2
\([\text{volume}] \neq 30, 60, 100, 250\)
A correct answer with no supportive working gets 0 marks
If an answer is shown in the range in working and then incorrectly rounded award full marks