Question

the radius of the cone is 1.25 inches, and it’s height is 2.75 inches. if the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?

Answer 1

the volume of the cone that can be filled with flavored ice is
`4.43in^3` .

Explanation:

Here we have , the radius of the cone is 1.25 inches, and it’s height is 2.75 inches. if the diameter of the bubble gum ball is 0.5 inches, We need to find what is the closest approximation of the volume of the cone that can be filled with flavored ice. Let's find out:

We know that , Volume of cone is :

⇒
`Volume = V_1 = (1)/(3)\pi r^2h`

Putting values of r=1.25 inches & h= 2.75 inches we get :

⇒
`V_1 = (1)/(3)(3.14) (1.25)^2(2.75)`

⇒
`V_1 = 4.497in^3`

Now , Volume of sphere is :

⇒
`Volume = V_2 = (4)/(3)\pi r^3`

Putting r = 0.25 inches( D = r/2 = 0.5/2=0.25 ) we get :

⇒
`V_2 = (4)/(3)(3.14) (0.25)^3`

⇒
`V_2 = 0.0653in^3`

So , volume of the cone that can be filled with flavored ice:

⇒
`V_1-V_2 = 4.497-0.0653`

⇒
`V_1-V_2 = 4.43in^3`

Therefore , the volume of the cone that can be filled with flavored ice is
`4.43in^3` .