Support colum

Calculate the support column's volume and surface. It is shaped as a vertical quadrangular prism whose base is a rhombus with diagonals u1 = 102 cm and u2 = 64 cm. The column height is 1. 5m.

Correct answer:

V =  0.4896 m³
S =  4.2653 m²

Step-by-step explanation:

$$\begin{gathered} u_1=102\text{cm}\to \text{m}=102:100\text{m}=1.02\text{m} \\ {u}_2=64\text{cm}\to \text{m}=64:100\text{m}=0.64\text{m} \\ h=1.5\text{m} \\ {S}_1=\frac{u_1\cdot u_2}{2}=\frac{1.02\cdot 0.64}{2}=\frac{204}{625}=0.3264{\text{m}}^2 \\ V=S_1\cdot h=0.3264\cdot 1.5=0.4896{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} a=\sqrt{(u_1/2{)}^2+(u_2/2{)}^2}=\sqrt{(1.02/2{)}^2+(0.64/2{)}^2}\doteq 0.6021\text{m} \\ o=4\cdot a=4\cdot 0.6021\doteq 2.4083\text{m} \\ S=2\cdot S_1+o\cdot h=2\cdot 0.3264+2.4083\cdot 1.5=4.2653{\text{m}}^2 \end{gathered}$$

Try another example