Numeracy Higher November 2022 Unit 1 Q4
4. Melin is a company that packages flour for sale in supermarkets.
It packages the flour in cylindrical bags.
The area of the cross-section of each of these bags is 25 cm2.
(a) Write down an expression, in terms of \(\pi\), for the radius of the base of each of these bags. [2]
(b) Each bag has a volume of 500 cm3.
(i) Currently the bags are filled with flour at a rate of \(\frac{1}{4}\) of a bag per second.
Complete the following statement. [2]
Complete the following statement. [2]
Melin packages bags of flour at a rate of …………… cm3 per minute.
(ii) A new cylindrical bag is designed to have the same capacity and to be more stable.
Melin decides to increase the area of the cross-section of its original bags by 100%.
Calculate the height of this new bag. [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(\sqrt{\dfrac{25}{\pi}}\) or \(\dfrac{5}{\sqrt{\pi}}\) or \(\dfrac{\sqrt{25}}{\sqrt{\pi}}\) or equivalent | B2 | ISW Accept √(25 ÷ π) or 5 ÷ √π or √25 ÷ √π For B1 accept π given as 3.1(4...) B1 for sight of any of the following:
|
| Scheme | Marks | Comments |
|---|---|---|
| (i) 500 × 60 ÷ 4 or equivalent | M1 | May be seen in stages |
| 7500 (cm3 per minute) | A1 | Answer given within the statement takes precedence |
| (ii) 500 ÷ (2 × 25) or equivalent | M1 | May be seen in stages |
| 10 (cm) | A1 |