Ten years ago, John bought a rectangular prism-shaped ottoman and two matching cubic-shaped ottomans - NSC Mathematical Literacy - Question 3 - 2020 - Paper 1

The diameter of the ottoman's leg is given as 75 mm. To find the radius, use the formula:

$\text{Radius} = \frac{\text{Diameter}}{2}$

Calculating:

$\text{Radius} = \frac{75 \text{ mm}}{2} = 37.5 \text{ mm}$

Therefore, the radius of the ottoman's leg is 37.5 mm.

The height of one cubic-shaped ottoman is 50 cm. The total height including the legs (assuming leg height is given as 12 cm):

$\text{Total Height} = \text{Height} + \text{Height of leg}$

Calculating:

$\text{Total Height} = 50 \text{ cm} + 12 \text{ cm} = 62 \text{ cm}$

Thus, the total height of ONE cubic-shaped ottoman is 62 cm.

The side surfaces for each ottoman need to be calculated:

• For the rectangular ottoman:

$\text{Area} = 2(\text{Length} + \text{Width}) \times \text{Height}$

Calculating:

$\text{Area} = 2(120 + 50) \times 50 = 2 \times 170 \times 50 = 17,000 \text{ cm}^2$

• For each cubic-shaped ottoman:

$\text{Area (one)} = 4 \times \text{Side}^2$

Calculating for one cubic-shaped ottoman:

$\text{Area (one)} = 4 \times 50^2 = 4 \times 2500 = 10,000 \text{ cm}^2$

Thus for two cubic-shaped ottomans:

$\text{Total Area (two)} = 2 \times 10,000 = 20,000 \text{ cm}^2$

Total area to be painted is:

$\text{Total Surface Area} = 17,000 + 20,000 = 37,000 \text{ cm}^2$

Therefore, the total surface area of the side surfaces of all ottomans that need to be painted is 37,000 cm².

The total area to be painted is 37,000 cm². With a paint coverage of 8 m² per litre, we first convert the area to m²:

$\text{Area in m²} = \frac{37,000 \text{ cm}^2}{10,000} = 3.7 \text{ m}^2$

For two coats, the area becomes:

$\text{Total Area for 2 coats} = 3.7 \times 2 = 7.4 \text{ m}^2$

Calculating the amount of paint needed:

$\text{Amount of paint (litres)} = \frac{\text{Total Area}}{\text{Spread rate}} = \frac{7.4}{8} = 0.925 \text{ litres}$

Convert litres to millilitres:

$0.925 \text{ litres} = 0.925 \times 1000 = 925 \text{ ml}$

Therefore, the amount of paint needed is 925 millilitres.

The volume of the paint tin is 1 litre = 1,000 cm³, and the radius is given as 6.5 cm. Using the formula for volume:

$\text{Volume} = \pi \times (\text{Radius})^2 \times \text{Height}$

Rearranging to find height:

$\text{Height} = \frac{\text{Volume}}{\pi \times (\text{Radius})^2}$

Calculating:

$\text{Height} = \frac{1000}{3.142 \times (6.5)^2}$

Calculating the radius squared:

$\text{Height} = \frac{1000}{3.142 \times 42.25} \approx \frac{1000}{133.78} \approx 7.47 \text{ cm}$

Thus, the height of the paint tin is approximately 7.47 cm.