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+2 20  50b=2b2+20b+2 20 2b2+30b40=0 2b230b+40=0 2 ...  prime number 30=235 40=235 GCD(2,30,40)=2  b215b+20=0  p=1;q=15;r=20 D=q24pr=1524120=145 D>0  b1,2=2pq±D=215±145 b1,2=7.5±6.020797 b1=13.520797289 b2=1.479202711  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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