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Li is going to paint a door that measures $195cm$ by $74cm$. He is going to give it two layers of paint on each side. One tin of paint covers $5{{m}^{2}}$. How many tins of paint does Li need to buy?

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Last updated date: 21st Jul 2024
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Answer
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Hint: We first convert the unit of measurement of blocks and the path in the same measurement unit. We find their area that is being painted twice on both sides. Then we divide the area with the tin’s amount of paint that covers $5{{m}^{2}}$. We find the number that is required.

Complete step-by-step solution:
We have dimensions of the door that is $195cm$ by $74cm$.
To solve the problem, we first take the same measurement unit for the door and capacity of the paint in the tin to cover.
We consider them all in meters. We divide the values by 100 to convert to metre from centimetre.
So, the dimensions of the door will be $\dfrac{195}{100}=1.95$m long and $\dfrac{74}{100}=0.74$m wide each.
The area of the door will be for one side. We are painting both sides twice for double layer painting.
The area of the door is $1.95\times 0.74=1.443{{m}^{2}}$.
The area that is being painted is $1.443\times 2\times 2=5.772{{m}^{2}}$.
Now we divide the area with the tin’s amount of paint that covers $5{{m}^{2}}$.
The number of tins required is $\dfrac{5.772}{5}=1.1544$.
So, we need at least 1 tin and then for the rest one more. In total 2 tins.

Note: We also could have changed the unit after finding the area but in that case, we should have divided the area by $100\times 100=10000$ instead of 100 as area becomes two dimensional.