Base of house

Calculate the volume of the bases of a square house. If the base depth is 1.2 m, the width is 40 cm, and the outer circumference is 40.7 m.

Correct answer:

V =  18.768 m³

Step-by-step explanation:

$$\begin{gathered} h=1.2\text{m} \\ s=40\text{cm}\to \text{m}=40:100\text{m}=0.4\text{m} \\ o=40.7\text{m} \\ a=o/4=40.7/4=\frac{407}{40}=10.175\text{m} \\ b=a-2\cdot s=10.175-2\cdot 0.4=\frac{75}{8}=9.375\text{m} \\ {S}_1=a^2=10.175^2\doteq 103.5306{\text{m}}^2 \\ {S}_2=b^2=9.375^2=\frac{5625}{64}\doteq 87.8906{\text{m}}^2 \\ S=S_1-S_2=103.5306-87.8906=\frac{391}{25}=15.64{\text{m}}^2 \\ V=S\cdot h=15.64\cdot 1.2=18.768{\text{m}}^3 \end{gathered}$$

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