1) The length, breadth and height of a cuboid are in the ratio 3:4:6 and volume of the cuboid is 576cm. Find the total surface area of the cuboid.
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Given ratio of l:b:h = 3:4:6
Let l =3x cm
b= 4x cm
h= 6x cm
Volume of a cuboid = 576 cm^3
l*b*h= 576
3x*4x*6x= 576
x^3 =576/(3*4*6)
After cancellation
x^3 =8
x^3= 2^3
x =2
Therfore l =3x = 3*2= 6 cm
b= 4x= 4* 2 = 8cm
h = 6x = 6*2 =12 cm
Total surface area of cuboid = 2(lb+bh+lh)
=2(6*8+8*12+6*12)
=2(48+96+72)
=2*216
=432 cm^2
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