Question

A square room contains 220.5 cu. m. of air. If the cost of colouring its 4 walls at
Rs 55 per sq. metre is Rs 6,930, find the height of the room.

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Answer 1

Answer:

Height = 4.5 Meters

Step-by-step explanation:

Its given that the room is square, i.e of equal width and depth.

Let a be the width of the room and b its height.

The cost of painting the walls is Rs 6,930 at Rs 55 per square metre.

Therefore Area of 4 walls = 6930/55 = 126 $m^{2}$

The total area of the walls is 4ab.

4ab = 126 $m^{2}$

ab = 31.5 $m^{2}$ which is area of each wall

Its given that

b$a^{2}$ = 220.5 $m^{3}$

a x ab = 220.5 $m^{3}$

a x 31.5 = 220.5

a = 220.5/31.5

a = 7 Meters

ab = 31.5

7b = 31.5

b = 31.5/7

b = 4.5 Meters

Height = 4.5 Meters