Pillar - bricks

A brick pillar has the shape of a four-sided prism with an isosceles trapezoid base with parallel sides a = 55 cm and c = 33 cm, leg b = 33 cm, and trapezoid height vₐ = 32.1 cm. The pillar is 1.9 m high. How many bricks were used to build it if one brick has a volume of 1,200 cm³? What area of the pillar must be painted if the bases are not included?

Final Answer:

n =  1342
S =  2.926 m²

Step-by-step explanation:

$$\begin{gathered} a=55\text{cm}\to \text{m}=55:100\text{m}=0.55\text{m} \\ c=33\text{cm}\to \text{m}=33:100\text{m}=0.33\text{m} \\ b=33\text{cm}\to \text{m}=33:100\text{m}=0.33\text{m} \\ {v}_1=32.1\text{cm}\to \text{m}=32.1:100\text{m}=0.321\text{m} \\ h=1.9\text{m} \\ {V}_1=200{\text{cm}}^3\to {\text{m}}^3=200:1000000{\text{m}}^3=0.0002{\text{m}}^3 \\ {S}_1=\frac{a+c}{2}\cdot v_1=\frac{0.55+0.33}{2}\cdot 0.321\doteq 0.1412{\text{m}}^2 \\ V=S_1\cdot h=0.1412\cdot 1.9\doteq 0.2684{\text{m}}^3 \\ n=\lceil V/V_1\rceil =\lceil 0.2684/0.0002\rceil =1342 \end{gathered}$$

$$\begin{gathered} o=a+b+c+b=0.55+0.33+0.33+0.33=\frac{77}{50}=1.54\text{m} \\ S=o\cdot h=1.54\cdot 1.9=2.926{\text{m}}^2 \end{gathered}$$

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