Cuboid - volume, diagonals

The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?

Correct result:

V =  144 cm3

Solution:

a=3 cm u1=5 cm b=u12a2=5232=4 cm c=132u12=13252=12 cm V=a b c=3 4 12=144 cm3a=3 \ \text{cm} \ \\ u_{1}=5 \ \text{cm} \ \\ b=\sqrt{ u_{1}^2-a^2 }=\sqrt{ 5^2-3^2 }=4 \ \text{cm} \ \\ c=\sqrt{ 13^2-u_{1}^2 }=\sqrt{ 13^2-5^2 }=12 \ \text{cm} \ \\ V=a \cdot \ b \cdot \ c=3 \cdot \ 4 \cdot \ 12=144 \ \text{cm}^3



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