The sum of the length,breadth and height of a cuboid is 21 cm and the lenght of the diagonal is 13cm. find the surface area of the cuboid.also find the cost of painting the surface at the rate of 1.40cm2.

the dimensions of the cuboid are in the ratio 3:2:2 and the lateral surface area of the cuboid is 2000m2.the outer surface of the cuboid is painted with enamel at the rate of 8 per m2.find the total cost of the painting the outer surface of the cuboid.
plz be fast.it is very urgent.

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Answers

2014-11-16T19:06:58+05:30

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1.
diagonal = √l²+b²+h² = 13
⇒l²+b²+h² = 13² = 169

l+b+h=21
⇒(l+b+h)²=21² = 441
⇒l²+b²+h²+2(lb+bh+lh)=441
⇒169 +  total surface area = 441
⇒ TSA = 441-169 = 272 cm²
cost = 272×1.40 = Rs. 380.8

2.
ratio = 3:2:2
length = 3x
breadth = 2x
height = 2x

the lateral surface area of the cuboid is 2000m2
4(3x×2x) = 2000
⇒24 x² = 2000
⇒ x² = 2000/24

TSA = 2(lb+bh+lh) = 2(3x×2x + 2x×2x + 2x×3x)
        =2(6x²+4x²+6x²)
        =2×16x² = 32x²
        = 32×(2000/24)
        =64000/24 m²
cost = 8×64000/24 = Rs. 21333.33

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