If 5 liters of paint cover an area of 13 m² and the rectangular tank needs 3 coats of painting, calculate the number of liters of paint needed to paint the tank as well as the number of 5 liter tins needed.
Answer (2)
Calculate the paint coverage rate: 2.6 m 2 / litre .
Determine the total area to be painted: 3 A , where A is the surface area of the tank.
Calculate the total litres of paint needed: 13 15 A litres.
Calculate the number of 5-litre tins needed: ⌈ 13 3 A ⌉ .
The amount of paint needed is 13 15 A litres and the number of 5-litre tins needed is ⌈ 13 3 A ⌉ .
Explanation
Problem Analysis Let's break down this painting problem step-by-step to make sure we get the right amount of paint!
Paint Coverage Rate First, we need to figure out how much paint is needed per square meter. We know that 5 litres of paint cover 13 square meters. So, we can find the coverage rate by dividing the area by the amount of paint:
Calculating Coverage Rate Coverage rate = 5 litres 13 m 2 = 2.6 m 2 / litre
Understanding Coverage This means each litre of paint covers 2.6 square meters.
Total Area to be Painted Now, let's say the surface area of the rectangular tank is A square meters. Since we need to apply 3 coats of paint, the total area to be painted is:
Calculating Total Area Total area = 3 × A
Litres of Paint Needed To find out how many litres of paint are needed for the total area, we divide the total area by the coverage rate:
Calculating Paint Needed Paint needed (litres) = 2.6 3 A = 26 30 A = 13 15 A
Number of Tins Needed Finally, to determine the number of 5-litre tins needed, we divide the total paint needed by 5 and round up to the nearest whole number because you can't buy part of a tin:
Calculating Number of Tins Number of tins = ⌈ 5 Paint needed ⌉ = ⌈ 13 × 5 15 A ⌉ = ⌈ 13 3 A ⌉
Final Answer So, to summarize, if the surface area of the tank is A m 2 :
Litres of paint needed: 13 15 A litres
Number of 5-litre tins needed: ⌈ 13 3 A ⌉
Examples
Imagine you're decorating your room and need to paint a wall. Knowing the paint coverage helps you estimate how much paint to buy. If one can of paint covers 10 square meters and you need to paint a wall that's 30 square meters, you'll need 3 cans of paint. This simple calculation ensures you don't run out of paint mid-project and helps you budget effectively. Understanding paint coverage is also useful for larger projects like painting houses, where accurate estimates can save significant costs.
To paint a rectangular tank requiring 3 coats, you will need 13 15 A liters of paint, where A is the surface area. The number of 5-liter tins needed is ⌈ 13 3 A ⌉ .
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