Body diagonal

Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm

Result

V =  35.37 cm3

Solution:

$u = 6.1 \ cm \ \\ a = 3.2 \ cm \ \\ b = 2.4 \ cm \ \\ \ \\ u = \sqrt{ a^2+b^2+c^2 } \ \\ \ \\ c = \sqrt{ u^2-a^2-b^2 } = \sqrt{ 6.1^2-3.2^2-2.4^2 } \doteq 4.6054 \ cm \ \\ \ \\ V = a \cdot \ b \cdot \ c = 3.2 \cdot \ 2.4 \cdot \ 4.6054 \doteq 35.3697 = 35.37 \ cm^3$

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