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Simphiwe makes candles as shown in the pictures below - NSC Mathematical Literacy - Question 3 - 2021 - Paper 1
Question 3
Simphiwe makes candles as shown in the pictures below. He uses a cylindrical mould to make the candles. He also carves horsesheads in some of the cylindrical candles... show full transcript
Worked Solution & Example Answer:Simphiwe makes candles as shown in the pictures below - NSC Mathematical Literacy - Question 3 - 2021 - Paper 1
Step 1
Determine the minimum length and width of the box he needs if the candles are tightly packed, touching each other in the box.
Answer
To find the dimensions of the box, we first calculate the diameter of the cylindrical candle:
- Diameter = 2 × radius = 2 × 5,2 cm = 10,4 cm.
Next, we can find the arrangement of the candles in a 4 by 3 grid. Therefore, the total width of the box will be:
- Width = 3 × diameter = 3 × 10,4 cm = 31,2 cm.
And for the length, since we have 4 candles:
- Length = 4 × diameter = 4 × 10,4 cm = 41,6 cm.
Step 2
Determine the number of candles he will be able to decorate with a 20-meter long ribbon.
Answer
First, we calculate the ribbon needed for one candle. The radius is 5,2 cm:
- Ribbon needed for one candle = 2 × 3,142 × 5,2 cm + 3 = 35,6768 cm.
Next, we convert 20 meters to centimeters:
- 20 meters = 2000 cm.
Now, we divide the total ribbon length by the ribbon needed for one candle:
- Number of candles = 2000 cm / 35,6768 cm ≈ 56 candles.
Step 3
Calculate the volume of wax needed for one horsehead candle.
Answer
To calculate the volume of the candle, we use the formula for the volume of a cylinder with radius 5,2 cm and height 11,4 cm:
- Volume = 3,142 × (5,2 cm)² × 11,4 cm ≈ 968,54 cm³.
Since the leftover wax filled up 1/3 of the mould:
- Volume of horsehead = 968,54 cm³ - (1/3 × 968,54 cm³) = 645,69 cm³.