Prism - box

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.

Result

S =  570 cm2

Solution:

a=7.5 u=12.5 V=0.9⋅ 103=900 b=u2−a2=12.52−7.52=10 c=V/(a⋅ b)=900/(7.5⋅ 10)=12 S=2⋅ (a⋅ b+b⋅ c+a⋅ c)=2⋅ (7.5⋅ 10+10⋅ 12+7.5⋅ 12)=570 cm2a=7.5 \ \\ u=12.5 \ \\ V=0.9 \cdot \ 10^3=900 \ \\ b=\sqrt{ u^2-a^2 }=\sqrt{ 12.5^2-7.5^2 }=10 \ \\ c=V/ (a \cdot \ b)=900/ (7.5 \cdot \ 10)=12 \ \\ S=2 \cdot \ (a \cdot \ b+b \cdot \ c+a \cdot \ c)=2 \cdot \ (7.5 \cdot \ 10+10 \cdot \ 12+7.5 \cdot \ 12)=570 \ \text{cm}^2

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