Answer:
145.8 cm³ of paint
Explanation:
d₁ = Smaller diameter paintball = 5 cm
d₂ = Larger diameter paintball = 9 cm
V₂ = Volume of larger diameter paintball
Volume of smaller diameter paintball
[tex]V_1=\frac{4}{3}\pi r_1^3\\\Rightarrow V_1=\frac{4}{3}\pi \left(\frac{d_1}{2}\right)^3\\\Rightarrow V_1=\frac{4}{24}\pi d_1^3[/tex]
Similarly
[tex]V_2=\frac{4}{24}\pi d_2^3[/tex]
Dividing the above two equations, we get
[tex]\frac{V_1}{V_2}=\frac{d_1^3}{d_2^3}\\\Rightarrow V_2=\frac{V_1}{\frac{d_1^3}{d_2^3}}\\\Rightarrow V_2=\frac{28}{\frac{125}{729}}\\\Rightarrow V_2=163.296\ cm^3[/tex]
∴ The larger one hold 163.296 cm³ of paint
