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The cost of painting the walls of a cubical room is ₹8640 at the rate of ₹15/m$^2$. Find the cost of painting the four walls of a cuboidal room having length 2 m more than the side of the cube, breadth 2 m less than the side of the cube, and height equal to the side of the cube. (The rate of painting is the same in both cases.)

1. ₹6480
2. ₹5600
3. ₹6820
4. ₹8640

Correct answer: ₹8640

Solution

From ₹8640 at ₹15/m$^2$, the painted area of the cube is 576 m$^2$. Since the four walls of a cube have area $4s^2$, we get $s=12$ m. For the cuboid, $l=14$, $b=10$, $h=12$, so four-wall area is $2\times 12\times(14+10)=576$ m$^2$, giving the same cost ₹8640.

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