Tsidi needs a bookshelf to store her files - NSC Mathematical Literacy - Question 3 - 2021 - Paper 2

To find B, we need to subtract the thickness of the bottom shelf and the top shelf from the total outside height of the bookshelf. The total outside height is 80 cm, the thickness of the bottom shelf is 4.5 cm, and the thickness of the top shelf is 1.5 cm:

$B = 80 ext{ cm} - (40 ext{ cm} + 1.5 ext{ cm})$

Calculating:

$B = 80 ext{ cm} - 41.5 ext{ cm} = 38.5 ext{ cm}$

To convert the total outside height of the bookshelf from inches to centimeters, we can use the conversion factor: 1 inch = 2.54 cm.

Therefore, the total outside height in cm is:

$ext{Total height in cm} = 31,496 ext{ inches} imes 2.54 ext{ cm/inch}$

Calculating:

$ext{Total height in cm} = 80 ext{ cm}$.

Hence, the conversion factor is approximately 2.54 cm per inch.

The area of one side of the backboard can be calculated using the formula for the area of a rectangle:

$ext{Area} = ext{width} imes ext{height}$

Given the width is 162 cm and the height is 80 cm, we have:

$ext{Area} = 162 ext{ cm} imes 80 ext{ cm} = 12,960 ext{ cm}^2$

To convert the area from cm² to m², we divide by 10,000 (since 1 m² = 10,000 cm²):

ext{Area in m}^2 = rac{12,960 ext{ cm}^2}{10,000} = 1.296 ext{ m}^2

To find the number of litres of paint required, we first divide the area to cover by the coverage per litre:

Given that 1 litre covers 6.9 m²:

ext{litres required} = rac{1.296 ext{ m}^2}{6.9 ext{ m}^2/ ext{ litre}}

Calculating:

$ext{litres required} = 0.1887 ext{ litres}$

Rounding to TWO decimal places, we get approximately 0.19 litres.

Tsidi's statement claims that one 500 mL can of paint is sufficient:

Since 500 mL = 0.5 litres and we calculated that approximately 0.19 litres is needed, we can say:

0.5 litres > 0.19 litres, therefore her statement is valid and she has enough paint.

To determine the maximum number of filing boxes that fit on a shelf, we need to convert the width of the filing box to cm. Since the width is given as 345 mm, this is equivalent to:

$345 ext{ mm} = 34.5 ext{ cm}$

Now, the width of the shelf is 162 cm, so:

ext{Number of boxes} = rac{162 ext{ cm}}{34.5 ext{ cm}} ext{ (rounded down)}

Calculating:

$ext{Number of boxes} = 4.695 ext{ (which rounds down to 4 boxes)}$

If we know that a single file has a width of 8.1 cm, we can calculate the number of single files that fit on the same shelf:

ext{Number of files} = rac{162 ext{ cm}}{8.1 ext{ cm}} = 20

The difference in the number of files versus filing boxes is:

$20 - 4 = 16$

Therefore, she can fit 16 more single files than filing boxes.

Tsidi might prefer filing boxes because they offer better organization. Filing boxes can contain multiple files, making it easier to categorize and store documents, whereas single files can be more chaotic and less organized.

The area required for one filing box can be determined as follows:

Given that the width of a box is 34.5 cm and estimating the length, we can assume a standard filing box length of approximately 24 cm. Therefore, the area of one filing box:

$ext{Area of one box} = 34.5 ext{ cm} imes 24 ext{ cm}$

Now, multiplying by the number of boxes:

$ext{Total area} = 4 ext{ boxes} imes (34.5 ext{ cm} imes 24 ext{ cm}) \ ext{or more specific box dimensions} \ = 4 ext{ boxes} imes 828 ext{ cm}^2$.

The total area for 4 filing boxes would be roughly 3312 cm².