Questions: Para chamar a atenção de seus clientes, uma empresa mandou instalar no pátio um monumento com o seu logotipo formado por paralelepípedos retângulos e com as medidas indicadas no desenho abaixo. V=6.3 .8 V=144 8 m V=3+2: 3 V=18

Para chamar a atenção de seus clientes, uma empresa mandou instalar no pátio um monumento com o seu logotipo formado por paralelepípedos retângulos e com as medidas indicadas no desenho abaixo.

V=6.3 .8
V=144

8 m

V=3+2: 3
V=18
Transcript text: Para chamar a atenção de seus clientes, uma empresa mandou instalar no pátio um monumento com o seu logotipo formado por paralelepípedos retângulos e com as medidas indicadas no desenho abaixo. \[ \begin{array}{l} V=6.3 .8 \\ V=144 \end{array} \] 8 m \[ V=3+2: 3 \] $V=18$
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Solution

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Solution Steps

Step 1: Identify the individual rectangular prisms

The monument is composed of three rectangular prisms. We need to calculate the volume of each prism separately.

Step 2: Calculate the volume of the first rectangular prism

The dimensions of the first rectangular prism are 6m (length) x 3m (width) x 8m (height). \[ V_1 = 6 \times 3 \times 8 = 144 \, \text{m}^3 \]

Step 3: Calculate the volume of the second rectangular prism

The dimensions of the second rectangular prism are 3m (length) x 2m (width) x 3m (height). \[ V_2 = 3 \times 2 \times 3 = 18 \, \text{m}^3 \]

Step 4: Calculate the volume of the third rectangular prism

The dimensions of the third rectangular prism are 2m (length) x 2m (width) x 3m (height). \[ V_3 = 2 \times 2 \times 3 = 12 \, \text{m}^3 \]

Step 5: Sum the volumes of the individual prisms

Add the volumes of the three prisms to get the total volume of the monument. \[ V_{\text{total}} = V_1 + V_2 + V_3 = 144 + 18 + 12 = 174 \, \text{m}^3 \]

Final Answer

The total volume of the monument is \( 174 \, \text{m}^3 \).

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