There are two different size spherical paintballs and the smaller one has a diameter of 5 cm and the larger one is 9 cm in diame

Question

Zigmanuir

3 months ago

13

There are two different size spherical paintballs and the smaller one has a diameter of 5 cm and the larger one is 9 cm in diame

ter. If the smaller paintball holds 28 cm3 of paint, how much does the larger one hold?

Physics

1 answer:

Ostrovityanka [3.2K] · Answer 1 · 2026-03-03T23:36:36+03:00

Answer:

145.8 cm³ of paint

Explanation:

d₁ = Diameter of the smaller paintball = 5 cm

d₂ = Diameter of the larger paintball = 9 cm

V₂ = Volume of the larger paintball

Volume of the smaller paintball

$V_1=\frac{4}{3}\pi r_1^3\\\Rightarrow V_1=\frac{4}{3}\pi \left(\frac{d_1}{2}\right)^3\\\Rightarrow V_1=\frac{4}{24}\pi d_1^3$

Likewise

$V_2=\frac{4}{24}\pi d_2^3$

By dividing the previous two equations, we derive

$\frac{V_1}{V_2}=\frac{d_1^3}{d_2^3}\\\Rightarrow V_2=\frac{V_1}{\frac{d_1^3}{d_2^3}}\\\Rightarrow V_2=\frac{28}{\frac{125}{729}}\\\Rightarrow V_2=163.296\ cm^3$

∴ The larger one accommodates 163.296 cm³ of paint