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Sagot :
Step 1; Identify the quantites
volume = V
Temperature = T
Pressure = P
[tex]\begin{gathered} V\text{ }\infty\frac{T}{P} \\ V\text{ = K }\frac{T}{P} \\ \text{Where K = constant of variation} \end{gathered}[/tex]V = 645, T = 430°, P = 10
Step 2 : substitute the value above into the formula to find the value of K
[tex]\begin{gathered} 645\text{ = k (}\frac{430}{10}) \\ 645\text{ = K (43)} \\ K\text{ = }\frac{645}{43} \\ K\text{ = 15} \end{gathered}[/tex]The relationship between the variables is given as
[tex]V\text{ = 15}\frac{T}{P}[/tex]Step 3: Find the volume, when T = 100°, P = 20
Then substitute the values into the relationship to find V
[tex]\begin{gathered} V\text{ = 15(}\frac{100}{20}) \\ V\text{ = }\frac{1500}{20} \\ V=\text{7}5 \end{gathered}[/tex]Therefore , volume V is 75
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