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The floor of a rectangular hall has a perimeter 250 m. If the cost of panting the four walls at the rate of Rs.10 per m^{2} is Rs.15000, find the height of the hall.

[**Hint: **Area of the four walls = Lateral surface area.]

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#### Solution

Let length, breadth, and height of the rectangular hall be* l* m, *b* m, and *h* m respectively.

Area of four walls = 2*lh* + 2*bh*

= 2(*l + b*) *h*

Perimeter of the floor of hall = 2(*l + b*)

= 250 m

∴ Area of four walls = 2(*l + b*) *h* = 250*h* m^{2}

Cost of painting per m^{2} area = Rs 10

Cost of painting 250*h* m^{2} area = Rs (250*h* × 10) = Rs 2500*h*

However, it is given that the cost of paining the walls is Rs 15000.

∴ 15000 = 2500*h*

*h* = 6

Therefore, the height of the hall is 6 m.

Concept: Surface Area of a Cuboid

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