Question

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

Answer 1

145.8 cm³ of paint

Step-by-step explanation:

d₁ = Smaller diameter paintball = 5 cm

d₂ = Larger diameter paintball = 9 cm

V₂ = Volume of larger diameter paintball

Volume of smaller diameter paintball

`V_1=(4)/(3)\pi r_1^3\\\Rightarrow V_1=(4)/(3)\pi \left((d_1)/(2)\right)^3\\\Rightarrow V_1=(4)/(24)\pi d_1^3`

Similarly

`V_2=(4)/(24)\pi d_2^3`

Dividing the above two equations, we get

`(V_1)/(V_2)=(d_1^3)/(d_2^3)\\\Rightarrow V_2=(V_1)/((d_1^3)/(d_2^3))\\\Rightarrow V_2=(28)/((125)/(729))\\\Rightarrow V_2=163.296\ cm^3`

∴ The larger one hold 163.296 cm³ of paint