Answer:
see explanation
Step-by-step explanation:
Given that p is inversely proportional to [tex]\sqrt[3]{V}[/tex] then the equation relating them is
p = [tex]\frac{k}{\sqrt[3]{V} }[/tex] ← k is the constant of proportion
To find k use the condition when V = 64, p = 6 , thus
6 = [tex]\frac{k}{\sqrt[3]{64} }[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
24 = k
p = [tex]\frac{24}{\sqrt[3]{V} }[/tex] ← equation of proportion
(a)
When V = 27, then
p = [tex]\frac{24}{\sqrt[3]{27} }[/tex] = [tex]\frac{24}{3}[/tex] = 8
(b)
When p = 2, then
2 = [tex]\frac{24}{\sqrt[3]{V} }[/tex] ( multiply both sides by [tex]\sqrt[3]{V}[/tex] )
2[tex]\sqrt[3]{V}[/tex] = 24 ( divide both sides by 2 )
[tex]\sqrt[3]{V}[/tex] = 12 ( cube both sides )
V = 12³ = 1728
