Ratio-cuboid

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

Final 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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You need to know the following knowledge to solve this word math problem:

algebrasolid geometryplanimetricsbasic operations and conceptsUnits of physical quantitiesGrade of the word problem

 
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