The floor of an office has dimensions $ 5 ext{ m} imes 3 ext{ m}$. The cost of painting the walls is ₹8,

Question

The floor of an office has dimensions $ 5 	ext{ m} 	imes 3 	ext{ m}$. The cost of painting the walls is ₹8,640 at the rate of ₹60/m $^2 $. Find the height of the room (in m).

Examoogle · Accepted Answer

The correct answer is Option D: 9. Calculate the lateral surface area first: $Area = \frac{Total Cost}{Rate} = \frac{8640}{60} = 144$ m². Then use $2(5+3)h = 144$, which simplifies to $16h = 144$, so $h = 9$ m.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate the lateral surface area first: $Area = \frac{Total Cost}{Rate} = \frac{8640}{60} = 144$ m². Then use $2(5+3)h = 144$, which simplifies to $16h = 144$, so $h = 9$ m.

Formula Used: $$Cost = Area_{walls} 	imes Rate = 2(l + w)h 	imes Rate$$

Given: Floor dimensions length l = 5 m, width w = 3 m. Total painting cost = ₹8,640. Rate of painting = ₹60/m².

Steps: Calculate the surface area of the walls: The surface area of the four walls is obtained by dividing the total painting cost by the rate per square meter.. Apply lateral surface area formula: The lateral surface area of a room is given by the formula $2(l + w)h$, where $l=5$ and $w=3$.. Solve for height $h$: Simplify the equation: $144 = 2(8)h = 16h$. Then $h = 144 / 16$.

Answer: D is correct because the calculated height of the room is 9 m.

Exam Tip: This problem relates to 3D geometry applications frequently seen in interior estimation, similar to volume and surface area problems in physics thermodynamics.

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