What volume of alcohol with a density of $$ 8.4 imes 10^{2} $$ $$ \mathrm{kgm}^{-3} $$ will have the sane mass as $$ 4.2 \mathrm{~m}^{3} $$ of petrol clensity is $$ 7.2 imes 10^{2} \mathrm{kgm}^{-3} $$ ?

Question

What volume of alcohol with a density of $$ 8.4 	imes 10^{2} $$ $$ \mathrm{kgm}^{-3} $$ will have the sane mass as $$ 4.2 \mathrm{~m}^{3} $$ of petrol clensity is $$ 7.2 	imes 10^{2} \mathrm{kgm}^{-3} $$ ?

UpStudy AI · Accepted Answer

To determine the volume of alcohol that has the same mass as a given volume of petrol, follow these steps:

1. **Calculate the Mass of the Petrol:**

$$
   \text{Mass}_{\text{petrol}} = \text{Density}_{\text{petrol}} \times \text{Volume}_{\text{petrol}}
   $$
   
   Given:
   - Density of petrol, $$\rho_{\text{petrol}} = 7.2 \times 10^{2} \, \text{kg/m}^3$$
   - Volume of petrol, $$V_{\text{petrol}} = 4.2 \, \text{m}^3$$
   
   $$
   \text{Mass}_{\text{petrol}} = 7.2 \times 10^{2} \, \text{kg/m}^3 \times 4.2 \, \text{m}^3 = 3024 \, \text{kg}
   $$

2. **Determine the Required Volume of Alcohol:**

$$
   V_{\text{alcohol}} = \frac{\text{Mass}_{\text{petrol}}}{\text{Density}_{\text{alcohol}}}
   $$
   
   Given:
   - Density of alcohol, $$\rho_{\text{alcohol}} = 8.4 \times 10^{2} \, \text{kg/m}^3$$
   
   $$
   V_{\text{alcohol}} = \frac{3024 \, \text{kg}}{8.4 \times 10^{2} \, \text{kg/m}^3} = \frac{3024}{840} = 3.6 \, \text{m}^3
   $$

**Answer:**  
A volume of 3.6 m³ of alcohol will have the same mass as 4.2 m³ of petrol.
A volume of 3.6 m³ of alcohol has the same mass as 4.2 m³ of petrol.

What volume of alcohol with a density of \( 8.4 \times 10^{2} \) \( \mathrm{kgm}^{-3} \) will have the sane mass as \( 4.2 \mathrm{~m}^{3} \) of petrol clensity is \( 7.2 \times 10^{2} \mathrm{kgm}^{-3} \) ?

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