Quadrilateral 70294

The edge lengths of a quadrilateral prism are in the ratio a: b: c = 2: 4: 5. The surface of the prism is 57 cm2. Calculate the volume.

Correct answer:

V =  25.9808 cm3

Step-by-step explanation:

a:b:c=2:4:5 S=57 cm2  a=2x b=4x c=5x  S=2(ab+bc+ca) S/2=2x 4x+4x 5x+5x 2x S/2=8x2+20x2+10x2  x=2 (8+20+10)S=2 (8+20+10)570.866 cm  a=2 x=2 0.866=3 cm1.7321 cm b=4 x=4 0.866=2 3 cm3.4641 cm c=5 x=5 0.8664.3301 cm  V=a b c=1.7321 3.4641 4.3301=15 325.9808 cm3   Verifying Solution:   S1=2 (a b+b c+c a)=2 (1.7321 3.4641+3.4641 4.3301+4.3301 1.7321)=57 cm2

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