A box contains 200 matches, correct to the nearest ten matches - OCR - GCSE Maths - Question 12 - 2023 - Paper 6

Given:

• Length (L) = 7 cm, correct to the nearest cm, implies: $6.5 \leq L < 7.5$
• Width (W) = 5 cm, correct to the nearest cm, implies: $4.5 \leq W < 5.5$
• Volume (V) = 248 cm³, correct to the nearest cm³, implies: $247.5 \leq V < 248.5$

We know that: $V = L \times W \times H$ Hence, $H = \frac{V}{L \times W}$

To find the minimum height, we would seek to minimize $H$:

1. Calculate the maximum possible values for L and W:
   • Maximum L = 7.5 cm
   • Minimum W = 4.5 cm
2. Substitute these in the expression of height: $H = \frac{247.5}{7.5 \times 4.5}$

Calculating $H$: $H = \frac{247.5}{33.75} \approx 7.33 \, \text{cm}$

Now, check the minimum possible case: 3. Calculate the minimum possible values for L and W:

• Minimum L = 6.5 cm
• Maximum W = 5.5 cm

4. Again substitute in the height expression: $H = \frac{247.5}{6.5 \times 5.5}$

Calculating $H$: $H = \frac{247.5}{35.75} \approx 6.92 \, \text{cm}$

Thus, the smallest possible height satisfying all the conditions is indeed: $H \geq 6 \, \text{cm}$