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=u2a2=12.527.52=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=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 = 570 \ cm^2







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Do you want to convert length units? Do you know the volume and unit volume, and want to convert volume units? Pythagorean theorem is the base for the right triangle calculator.