Question

The dimensions of a cuboid are in the ratio 3:2:2 and the lateral surface area of cuboid is 2000m^2 . The outer surface of the cuboid is painted with coloured enamel at the rate of Rs 8 per m square. Find the total cost of painting the outer surface of the cuboid

Plz i need full explanation

Answer 1

Answer:

We are given that the dimensions of cuboid are 3:2:2

Let the ratio be x

So, length = 3x

Breadth = 2x

Height = 2x

Lateral surface area of cuboid = 2(l+b)h2(l+b)h

= 2(3x+2x)2x2(3x+2x)2x

Since we are given that the lateral surface area of cuboid is 2000 sq.m.

So, 2000=20x^22000=20x

2

200=2x^2200=2x

2

100=x^2100=x

2

10=x10=x

So, length = 3x = 3\times 10 = 303x=3×10=30

Breadth = 2x = 2\times 10 = 202x=2×10=20

Height = 2x = 2\times 10 = 202x=2×10=20

Total Surface area of cuboid = 2(lb+bh+hl)2(lb+bh+hl)

= 2(30\times 20+20\times 20+30\times 20)2(30×20+20×20+30×20)

= 3200 m^23200m

2

Cost painting 1 sq.m. = Rs.8

Cost of painting the 3200 sq.m. = 8 \times 3200=56008×3200=5600

Thus the total cost of painting the outer surface of the cuboid is Rs.5600.

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