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

First, calculate the area of the circular hole using the formula:

ext{Area of circle} = rac{22}{7} imes (9.5 ext{ cm})^2 \ = 3,142 imes 90.25 ext{ cm}^2 \ = 283,565625 ext{ cm}^2

The block has 6 faces, and 2 of those faces have holes, so we can calculate the total areas:

• 2 faces with holes:

$$2 imes (2025 ext{ cm}^2 - 283,565625 ext{ cm}^2) = 2 imes 1741,434375 ext{ cm}^2 = 3482,86875 ext{ cm}^2$$

• 4 faces without holes:

$$4 imes 2025 ext{ cm}^2 = 8100 ext{ cm}^2$$

Now add the areas:

$$ext{Total Surface Area} = 8100 ext{ cm}^2 + 3482,86875 ext{ cm}^2 = 11 582,86875 ext{ cm}^2 \ ext{(Rounded: 11 582,869)}$$

The total surface area for 12 chairs is:

$$11 582,869 ext{ cm}^2 imes 12 = 139,894,428 ext{ cm}^2$$

The amount of paint required: Given the spread rate of 1.8 m² per 15 cm², we must convert as follows:

First, convert m² to cm²:

$$1.8 ext{ m}^2 = 18,000 ext{ cm}^2$$

Then, calculate the total paint required:

ext{Amount of paint} = rac{139,894,428 ext{ cm}^2}{18,000 ext{ cm}^2} \ ext{(about 776.5)} = 777 ext{ L}

Rounding to the nearest litre gives approximately 777 litres needed for painting.

The diameter of the tin can be found using the formula:

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

Given the volume of the tin and using the formula for the volume of a cylinder, we can set up the following:

Volume = ext{base area} imes ext{height} \ 5 000 ext{ cm}^3 = rac{22}{7} imes (7 ext{ cm})^2 imes ext{height}

Where the base area calculates to:

= rac{22}{7} imes 49 ext{ cm}^2 = 154 ext{ cm}^2

Solving for height gives:

ext{height} = rac{5000}{154} = 32.47 ext{ cm}

So, the height of the paint in the tin is approximately 32.47 cm.