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Ten years ago, John bought a rectangular prism-shaped ottoman and two matching cubic-shaped ottomans - NSC Mathematical Literacy - Question 3 - 2020 - Paper 1
Question 3
Ten years ago, John bought a rectangular prism-shaped ottoman and two matching cubic-shaped ottomans. He wants to refurbish each of them by having the side surfaces ... show full transcript
Worked Solution & Example Answer:Ten years ago, John bought a rectangular prism-shaped ottoman and two matching cubic-shaped ottomans - NSC Mathematical Literacy - Question 3 - 2020 - Paper 1
Step 1
3.1.1 Determine the total number of legs for the ottomans John has to purchase.
Answer
To determine the total number of legs:
- The rectangular prism-shaped ottoman has 6 legs.
- Each of the two cubic-shaped ottomans has 4 legs. Therefore, for two cubic ottomans, the total is legs.
Adding these together gives:
Total legs = 6 + 8 = 14 legs.
Step 2
Step 3
3.1.3 Calculate, in centimetres, the total height (including the legs) of ONE cubic-shaped ottoman.
Answer
The height of one cubic-shaped ottoman is given as 50 cm. The total height including the leg is:
Total height = Height of ottoman + Height of leg
The leg height is given as 12 cm, thus:
Total height = 50 cm + 12 cm = 62 cm.
Step 4
3.1.4 Calculate, in cm², the total surface area of the side surfaces of all items that need to be painted.
Answer
For two cubic-shaped ottomans, the surface area can be calculated as follows:
- Area of one cubic ottoman's side surfaces = 4 sides × (side × height) = 4 × (50 cm × 50 cm) = 10,000 cm².
- Total for two cubic ottomans: 2 × 10,000 cm² = 20,000 cm².
For the rectangular ottoman, the side surfaces area is calculated using its dimensions:
- Area of rectangular ottoman's side surfaces = 2 × (length × height + width × height) = 2 × (120 cm × 50 cm + 50 cm × 50 cm) = 2 × (6000 cm² + 2500 cm²) = 19,000 cm².
Total area to be painted = 20,000 cm² + 19,000 cm² = 39,000 cm².
Step 5
3.1.5 Calculate, in millilitres, the amount of paint required to paint ALL the ottomans with TWO coats of paint.
Answer
The spread rate of the paint is provided as 7.4 m² per litre. Therefore:
- Total area to paint = 39,000 cm² = 3.9 m².
- Amount of paint for 1 coat = ( \frac{39,000 \text{ cm}^2}{7.4 \text{ m}^2} = 5,270.27 \text{ ml} )
- For 2 coats, multiply by 2: 5,270.27 mL × 2 = 10,540.54 mL.
Thus, the total amount of paint required is approximately 10,541 mL.
Step 6
3.1.6 Calculate the height (in cm) of the paint in the tin.
Answer
Given the inner radius of the tin is 6.5 cm:
Volume of the tin = 1,000 cm³. Using the volume formula:
Height = Volume / (3.142 × (radius)²)
Plugging in the values: Height = ( \frac{1000}{3.142 \times (6.5)^2} \approx 24.45 ext{ cm} )