A box contains 200 matches, correct to the nearest ten matches. (a) Complete the error interval for n, the number of matches in the box. (b) The box is a cuboid with • length 7 cm, correct to the nearest cm • width 5 cm, correct to the nearest cm • volume 248 cm³, correct to the nearest cm³. Show that the smallest possible height of the box is 6 cm.

GCSE OCR Maths Volume: A box contains 200 matches, corr

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

Question 12

A box contains 200 matches, correct to the nearest ten matches. (a) Complete the error interval for n, the number of matches in the box. (b) The box is a cuboid wi... show full transcript

Worked Solution & Example Answer:A box contains 200 matches, correct to the nearest ten matches - OCR - GCSE Maths - Question 12 - 2023 - Paper 6

Step 1

(a) Complete the error interval for n, the number of matches in the box.

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Answer

To determine the error interval for n, we consider the fact that the box contains 200 matches, correct to the nearest ten matches.

The possible values of n range from half of the precision band below and above 200:

The lower limit is 200 - 5 = 195.
The upper limit is 200 + 5 = 205.

Therefore, the error interval is:

$195 \, \leq n \leq 205$

Step 2

(b) Show that the smallest possible height of the box is 6 cm.

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Answer

Given:

Length (l) = 7 cm ± 0.5 cm, so the range for length is 6.5 cm to 7.5 cm.
Width (w) = 5 cm ± 0.5 cm, so the range for width is 4.5 cm to 5.5 cm.
Volume (V) = 248 cm³ ± 0.5 cm³.

We can calculate the height (h) using the formula for the volume of a cuboid:

$V = l \times w \times h$

To find the smallest possible height, we will use the largest possible values for length and width:

Maximum length = 7.5 cm and maximum width = 5.5 cm
Calculate height:

$(h = \frac{V}{l \times w})$

Substituting our values:

$h = \frac{248}{7.5 \times 5.5}$

$h = \frac{248}{41.25} \approx 6.00 \, \text{cm}$

Thus, the smallest possible height of the box is 6 cm.

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

Worked Solution & Example Answer:A box contains 200 matches, correct to the nearest ten matches - OCR - GCSE Maths - Question 12 - 2023 - Paper 6

(a) Complete the error interval for n, the number of matches in the box.

(b) Show that the smallest possible height of the box is 6 cm.

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