Question

Which of the following is the closest to the volume of the space within the cylinder that is outside the cone?

Answer 1

Given the figure of a cone inside a cylinder

The volume of the space between the cylinder and the cone = the volume of the cylinder - the volume of the cone

The volume of the cylinder =

`\pi\cdot r^2\cdot h`

The volume of the cone =

`(1)/(3)\cdot\pi\cdot r^2\cdot h`

So, the volume of the space between them =

`\pi\cdot r^2\cdot h-(1)/(3)\pi\cdot r^2\cdot h=(2)/(3)\pi\cdot r^2\cdot h`

As shown in the figure: r = 4/2 = 2 in

h = 6 in

Let pi = 3.14

So, substitute with r, h, and pi

The volume of the space =

`(2)/(3)\cdot3.14\cdot2^2\cdot6=50.24`

Rounding to the nearest whole number

So, the answer will be option B) 50 in^3