Question

Debbie buys a tree for the holidays. She would like to determine the amount of space it will take up in her living room. The tree is cone shaped and has a radius of 2 feet. Find the volume of the tree if it is in the shape of a cone and its height is two times its radius. The radius of a cone whose height is is equal to two times its radius is given as: r equal to cube root of (3V/4π)

Answer 1

Volume of Cone =

`= (1)/(3)\pi (2)^2 (4)\\\\=(1)/(3)(3.14)(4)(4)\\\\=(1)/(3)* 3.14* 16 \\\\=(1)/(3)*50.24\\\\=16.746\\\\\approx16.75 \texttt {ft} ^3`

Thus, Volume = 16.75 cubic feet

Explanation:

Volume of a cone is given by the formula

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

Where r is the radius and

h is the height

Given radius r = 2 and

height is 2 times that.

So height is 2*2 = 4

Plugging these into the formula we get:

Volume of Cone =

`= (1)/(3)\pi (2)^2 (4)\\\\=(1)/(3)(3.14)(4)(4)\\\\=(1)/(3)* 3.14* 16 \\\\=(1)/(3)*50.24\\\\=16.746\\\\\approx16.75 \texttt {ft} ^3`

Thus, Volume = 16.75 cubic feet