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A marble stone 20 cm long by 15 cm wide and 3 cm thick weighs 2.25 kg. How much will another marble stone 2.5 m long by 1.2 m wide and 15 cm thick weigh?

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Answer to a math question A marble stone 20 cm long by 15 cm wide and 3 cm thick weighs 2.25 kg. How much will another marble stone 2.5 m long by 1.2 m wide and 15 cm thick weigh?

Expert avatar
Sigrid
4.5
111 Answers
\text{Calculamos primeiro o volume do bloco de mármore original:}

V_{\text{original}} = 20 \, \text{cm} \times 15 \, \text{cm} \times 3 \, \text{cm}
V_{\text{original}} = 900 \, \text{cm}^3

\text{Agora, calculamos a densidade do mármore.}

\text{Densidade} = \frac{\text{massa}}{\text{volume}}
\text{Densidade} = \frac{2{,}25 \, \text{kg}}{900 \, \text{cm}^3}
\text{Densidade} = 0{,}0025 \, \text{kg/cm}^3

\text{Convertendo a densidade para metros cúbicos:}
1 \, \text{cm}^3 = 10^{-6} \, \text{m}^3
\text{Densidade} = 0{,}0025 \times 10^6 \, \text{kg/m}^3
\text{Densidade} = 2500 \, \text{kg/m}^3

\text{Calculamos o volume do bloco de mármore maior:}

V_{\text{maior}} = 2{,}5 \, \text{m} \times 1{,}2 \, \text{m} \times 0{,}15 \, \text{m}
V_{\text{maior}} = 0{,}45 \, \text{m}^3

\text{Finalmente, calculamos a massa do novo bloco:}

\text{Massa} = \text{Densidade} \times V_{\text{maior}}
\text{Massa} = 2500 \, \text{kg/m}^3 \times 0{,}45 \, \text{m}^3
\text{Massa} = 1125 \, \text{kg}

\text{Portanto, o bloco de mármore maior pesa 1125 kg.}

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