Ratio-cuboid

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

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Check out our ratio calculator.
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?
Tip: Our volume units converter will help you convert volume units.
See also our right triangle calculator.
See also our trigonometric triangle calculator.

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

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: