Question

The dimensions of a cuboidal room are in the ratio 4:5:6: and its total surface area is 5328 m sq . Find the dimensions and the cost of painting it at inside at rupees 20 per sq m.

Answer 1

Answer:

Step-by-step explanation:

Let the common ratio be x

l=4x, b=5x, h=6x

surface area = 2(lh+bh+lb)

=2(4x*5x+5x*6x*4x*6x)

=2(20x^2+30x^2+24x^2)

= 2 * 74x^2

= 148x^2m^2

148x^2 = 5328 m^2

x^2 = 5328/148 = 36

x  = $\sqrt{36}$ = 6

l = 4*6 = 24m

b=5*6 = 30m

h = 6*6 = 36m

Cost of painting=LSA*20

LSA = 2h(l+b)

= 2 * 36 (20+30)

= 72 * 50

= 3600m^2

cost = 3600*2 = Rs. 7200 Ans.

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