Solid cuboid

A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.

Correct answer:

d =  13.7477 cm

Step-by-step explanation:

V=40 cm3 S=100 cm2 a=2 cm V=abc S=2(ab+bc+ac)  20=bc 50=2b+bc+2c  20/b=c 50b=2b2+20b+220  50b=2b2+20b+2 20 2b2+30b40=0 2b230b+40=0  p=2;q=30;r=40 D=q24pr=3024240=580 D>0  b1,2=2pq±D=430±580=430±2145 b1,2=7.5±6.0207972893961 b1=13.520797289396 b2=1.4792027106039   Factored form of the equation:  2(b13.520797289396)(b1.4792027106039)=0  b=b1=13.520813.5208 cm c=20/b=20/13.52081.4792 cm  V1=a b c=2 13.5208 1.4792=40 cm3 S1=2 (a b+b c+a c)=2 (2 13.5208+13.5208 1.4792+2 1.4792)=100 cm2  d=a2+b2+c2=22+13.52082+1.47922=3 21=13.7477 cm

Our quadratic equation calculator calculates it.




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



avatar







Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a system of equations and looking for calculator system of linear equations?
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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

Related math problems and questions: