Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c has dimensions in the ratio of 7:8:10. If you know that the diagonal wall AC is 56 cm, and the angle between AC and space diagonal AG is 25 degrees.

Correct answer:

a =  18.28 cm
b =  20.89 cm
c =  26.11 cm
V =  9972 cm3
S =  2809 cm2

Step-by-step explanation:

a=56 tan25°/10 7=tan5π/36=18.28=18.28 cm
b=56 tan25°/10 8=tan5π/36=20.89=20.89 cm
tan25=ACc c=ACtan25=26.11 cm a=107c=18.28 b=108c=20.89 cm
V=abc=9972 cm3
S=2(ab+bc+ac)=2809 cm2

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