Cuboid edges

Calculate the volume and surface of a cuboid whose edge lengths are in the ratio 2: 3: 4 and the longest edge measures 10cm.

Correct result:

V =  375 cm3
S =  325 cm2

Solution:

a:b:c=2:3:4 a<b<c c=10 cm  c=4x x=c/4=10/4=52=2.5 a=2⋅ x=2⋅ 2.5=5 cm b=3⋅ x=3⋅ 2.5=152=7.5 cm  V=a⋅ b⋅ c=5⋅ 7.5⋅ 10=375 cm3a:b:c=2:3:4 \ \\ a<b<c \ \\ c=10 \ \text{cm} \ \\ \ \\ c=4x \ \\ x=c/4=10/4=\dfrac{ 5 }{ 2 }=2.5 \ \\ a=2 \cdot \ x=2 \cdot \ 2.5=5 \ \text{cm} \ \\ b=3 \cdot \ x=3 \cdot \ 2.5=\dfrac{ 15 }{ 2 }=7.5 \ \text{cm} \ \\ \ \\ V=a \cdot \ b \cdot \ c=5 \cdot \ 7.5 \cdot \ 10=375 \ \text{cm}^3
S=2⋅ (a⋅ b+b⋅ c+a⋅ c)=2⋅ (5⋅ 7.5+7.5⋅ 10+5⋅ 10)=325 cm2S=2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c)=2 \cdot \ (5 \cdot \ 7.5+7.5 \cdot \ 10+5 \cdot \ 10)=325 \ \text{cm}^2

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