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

To find B, we subtract the thickness of the bottom shelf (4.5 cm) and the thickness of the top shelf (1.5 cm) from the total outside height (80 cm):

$B = 80 ext{ cm} - 40 ext{ cm} - 1.5 ext{ cm} = 38.5 ext{ cm}$

Thus, the inside height B of the top shelf is 38.5 cm.

First, we convert the total height of the bookshelf from inches to centimeters:

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

Calculating this gives:

$31,496 ext{ inches} imes 2.54 ext{ cm/inch} = 80.00 ext{ cm}$

When divided by total inches:

$1 ext{ inch} = 2.54 ext{ cm}$

So the rounded conversion factors to TWO decimal places is 1 inch = 2.54 cm.

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

$ext{Area} = ext{Height} imes ext{Width}$

Here, the height is 80 cm and the width is 162 cm:

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

Therefore, the area of one side of the backboard is 12,960 cm².

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

ext{Area in m²} = rac{12,960 ext{ cm}^2}{10,000} = 1.296 ext{ m}²

Thus, the area is 1.296 m².

Given that 1 litre of paint covers 6.9 m², we first determine how many litres are required:

ext{Litres Required} = rac{ ext{Area}}{ ext{Coverage per Litre}} = rac{1.296 ext{ m}²}{6.9 ext{ m}²/ ext{L}} = 0.188 ext{ L}

Rounding to TWO decimal places, we find that Tsidi needs approximately 0.19 litres of paint.

Tsidi stated that one 500 mL can of paint is sufficient. Since 500 mL equals 0.5 L, we compare this with the required amount:

A required 0.19 L of paint is less than 0.5 L. Thus, her statement is valid.

To calculate the number of filing boxes that fit on one shelf:

First, convert the width of the filing box to centimeters: 345 mm = 34.5 cm.

Now, use the formula:

ext{Number of Boxes} = rac{162 ext{ cm}}{34.5 ext{ cm}} ext{ and rounded down} = 4 ext{ boxes}

Thus, a maximum of 4 filing boxes can fit on one shelf.

The number of single files that can fit on one shelf is given by:

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

To find the difference:

$ext{Difference} = 20 - 4 = 16$

Thus, Tsidi can fit 16 more single files than filing boxes.

One possible reason why Tsidi would prefer filing boxes is that they allow for better organization and protection of documents. Filing boxes can prevent documents from becoming damaged and help categorize files more effectively.

Assuming Tsidi has 1 shelf and 4 boxes, the probability that the shelf chosen contains the needed documents:

P( ext{correct box}) = rac{1}{4}

Therefore, the probability is 0.25, or 25%.