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 result:

d =  13.7477 cm

Solution:

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=q±D2p=30±5804=30±21454 b1,2=7.5±6.0207972894 b1=13.5207972894 b2=1.4792027106   Factored form of the equation:  2(b13.5207972894)(b1.4792027106)=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

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