# Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.

Result

V =  30
S =  62

#### Solution:

$\ \\ \ \\ 29=a^2+b^2 \ \\ 34=b^2+c^2 \ \\ 13=a^2+c^2 \ \\ \ \\ a^2=29 - b^2=29-34+c^2=29-34+13-a^2 \ \\ 2a^2=x^2-y^2+z^2 \ \\ \ \\ a=\sqrt{ \dfrac{ 29-34+13 }{ 2 } }=2 \ \\ \ \\ ... \ \\ b=\sqrt{ \dfrac{ 29+34-13 }{ 2 } }=5 \ \\ \ \\ ... \ \\ c=\sqrt{ \dfrac{ -29+34+13 }{ 2 } }=3 \ \\ \ \\ V=a \cdot \ b \cdot \ c=2 \cdot \ 5 \cdot \ 3=30$
$S=2 \cdot \ (a \cdot \ b+b \cdot \ c+c \cdot \ a)=2 \cdot \ (2 \cdot \ 5+5 \cdot \ 3+3 \cdot \ 2)=62$

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