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2.1.3 The block of wax is wrapped in a sticky plastic. The plastic wrap required to cover the entire Surface area of a block will include \( 20 \% \) of overlap. (a) Calculate the area of the plastic which will be required. (b) If a plastic wrap is sold at \( \mathrm{R} 1,20 / \mathrm{m}^{2} \), determine the total cost of plastic required

Ask by Zimmerman Morgan. in South Africa
Mar 11,2025

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Answer

(a) The area of plastic required is \( 1.20 \times A \) square meters. (b) The total cost of plastic required is \( 144A \) Rands.

Solution

Given: - The plastic wrap required to cover the entire surface area of the block will include 20% overlap. (a) To calculate the area of the plastic required: Let's assume the surface area of the block is \( A \) square meters. The area of the plastic required to cover the entire surface area of the block with 20% overlap is given by: \[ \text{Area of plastic required} = A + 0.20A = 1.20A \] (b) To determine the total cost of plastic required: The cost of plastic wrap is \( \mathrm{R} 1,20 / \mathrm{m}^{2} \). The total cost of plastic required is: \[ \text{Total cost} = \text{Area of plastic required} \times \text{Cost per square meter} \] Let's calculate the total cost of plastic required. Simplify the expression by following steps: - step0: Solution: \(1.2A\) Calculate or simplify the expression \( 1.2A \). Simplify the expression by following steps: - step0: Solution: \(1.2A\) The area of the plastic required is \( 1.2A \) square meters. Now, let's calculate the total cost of plastic required. Simplify the expression by following steps: - step0: Solution: \(1.2A\times 120\) - step1: Multiply the terms: \(144A\) The total cost of plastic required is \( 144A \) Rands.

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To determine the area of the plastic required to wrap the block of wax, we’ll first need to calculate the surface area of the block and then add 20% for overlap. Assuming the block of wax is in the shape of a rectangular prism with dimensions a, b, and h, the surface area (SA) can be calculated using the formula: \[ \text{SA} = 2(ab + ah + bh) \] After assessing the surface area, we add 20% overlap: \[ \text{Total Area} = \text{SA} \times 1.2 \] Next, for the total cost of the plastic, multiply the total area calculated by the cost per square meter: \[ \text{Total Cost} = \text{Total Area} \times \mathrm{R} 1.20 \] This calculation ensures that you have enough plastic to cover the block securely while accounting for any necessary overlap.

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