# Satish used 6 L of oil paint to paint a map of India of 6 m high. How many litres of paint would Santosh need for painting a proportionally scaled map of height 18 m? Please explain sol elaborately Ans - 54

Hi,
Here pay attention to the word- "proportionally scaled map", meaning the figures are similar.
.From the area theorem we know that areas of  two similar figure is in the same ratio as that of square of their heights
So, If the heights of maps are in the ratio
=$\frac{6}{18}=\frac{1}{3}$

Area will be in the ratio of =$\frac{{1}^{2}}{{3}^{2}}=\frac{1}{9}$
Now for denominator's 1 square unit paint used = 6 liters
so for denominator's 9 square unit paint used will be = 6*9 = 54 litres

. Therefore, the quantity (of paint) required to paint the map that is 18 metres high54 litres

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