Cuboid

Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.

Result

b =  30 cm
c =  5 cm

Solution:

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$c=c_{2}=5 \ \text{cm} \ \\ \ \\ \text{ Correctness test: } \ \\ d=\sqrt{ a^2+b^2+c^2 }=\sqrt{ 6^2+30^2+5^2 }=31 \ \\ d=u \ \\ V_{2}=a \cdot \ b \cdot \ c=6 \cdot \ 30 \cdot \ 5=900 \ \text{cm}^3 \ \\ V_{2}=V$

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