The Bambanani Crèche in Bethlehem bought the cube blocks below from an auction - NSC Mathematical Literacy - Question 3 - 2019 - Paper 1

To calculate the total surface area:

1. Calculate the area of the face with the hole, using the formula:

   ext{Area of circle} = rac{22}{7} imes (9.5 ext{ cm})^2 \n = 3.142 imes 90.25 ext{ cm}^2 \n \\ = 283.56 ext{ cm}^2

2. Area of one face with hole = Area of square - Area of circle:

   $$ext{Area with hole} = 2025 ext{ cm}^2 - 283.56 ext{ cm}^2 \n = 1741.44 ext{ cm}^2$$

3. Total area of 12 chairs:

   • There are 6 sides without holes and 6 sides with holes:
   • Total portion with holes = 6 x 1741.44 cm² + 6 x 283.56 cm² = 10448.64 cm² + 1701.36 cm² = 11,582.00 cm² Thus, we have shown the total surface area is approximately 11,582.869 cm².

Given that the total surface area needing paint is 11,582.869 cm² and the paint coverage per litre:

1. Total area covered by 1 litre of paint:
   • Coverage = 1.8 m² = 1.8 × 10,000 cm² = 18,000 cm²
2. Required paint in litres: ext{Total paint} = rac{11,582.869 ext{ cm}^2}{18000 ext{ cm}^2/ ext{ litre}} \ ext{Total paint} ext{ (litres)} = 0.6434 ext{ litres}\

Round it up to the nearest litre:

• Total paint needed = 1 litre.

The diameter of the tin is calculated as follows:

$$ext{Diameter} = 2 imes ext{radius} = 2 imes 7 ext{ cm} = 14 ext{ cm}$$

To find the height of the paint in the tin, we first calculate the volume of the tin:

1. Volume of the cylinder: ext{Volume} = rac{22}{7} imes (7 ext{ cm})^2 imes ext{height} = 147 ext{ cm}^2 imes ext{height}
2. Set the volume equal to 5000 cm³: 147 imes ext{height} = 5000 \ ext{height} = rac{5000}{147} \ ext{height} ext{ (cm)} ext{ is approximately } 34.0 ext{ cm}