The lengths of the edges of the cuboid are in the ratio 2:3:6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.

Correct answer:

V =  288 cm3
S =  288 cm2

Step-by-step explanation:

a:b:c = 2:3:6 a= 2x b = 3x c = 6x u=14 cm  u = a2+b2+c2 u = (2x)2+(3x)2+(6x)2 u = 4x2+9x2+36x2 u2 = 4x2+9x2+36x2  x=u/4+9+36=14/4+9+36=2 cm a=2 x=2 2=4 cm b=3 x=3 2=6 cm c=6 x=6 2=12 cm u2=a2+b2+c2=42+62+122=14 V=a b c=4 6 12=288 cm3
S=2 (a b+b c+a c)=2 (4 6+6 12+4 12)=288 cm2

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