Question

The dimensions of a cuboidal room are in
the ratio 4:5:6 and its total surface area is
5328m². Find the dimensions and the cost
А
of painting it at inside at *20 per sq metre. c​

Answer 1

Answer:

Height of the room = 4x = 24m

Breadth of the room = 5x = 30m

Length of the room = 6x = 36m

Inside Area to be painted = Total surface area - the floor area $= 5328m^2 - (30)(36)m^2$ $= 4248m^2$

@20 per square metre, the cost of painting inside area $= (4248)(20) = 84,960$

Step-by-step explanation:

The dimensions of a cuboidal room are in the ratio 4:5:6

Let's assume the proportionality constant is x

Therefore, total surface area = 2(4x.5x + 5x.6x + 6x.4x) $= 2 (74x^2) = 148x^2$

According to the problem:

$148x^2 = 5328$

∴ $x^2 = \frac{5328}{148} = 36$

∴ $x = 6$

∴ Height of the room = 4x = 24m

Breadth of the room = 5x = 30m

Length of the room = 6x = 36m

Inside Area to be painted = Total surface area - the floor area $= 5328m^2 - (30)(36)m^2$ $= (5328 - 1080)m^2 = 4248m^2$

@20 per square metre, the cost of painting inside area $= (4248)(20) = 84,960$