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 4 feet. Find the volume of the tree if it is in the shape of a cone and its height is three times its radius. The radius of a cone whose height is is equal to three times its radius is given as: r=root(frac(3V,3π),3) (Use π=3.14)

Answer 1

Volume of cone = 200.96 square feet

Explanation:

We are given the following information in the question:

The tree is cone shaped and has a radius of 4 feet.

r = 4 feet

The height of the tree is three times its radius.

`h = 3* r = 3* 4 = 12\text{ feet}`

Volume of tree =

`\text{Volume of cone} = \displaystyle(1)/(3)\pi r^2 h`

Putting all the values, we get,

`\text{Volume of tree} = \displaystyle(1)/(3)\pi (4)^2 (12)\\\\= (1)/(3)* 3.14* 4* 4* 12 = 200.96\text{ square feet}`

Radius of cone whose height is is equal to three times its radius is given as:

`V =  \displaystyle(1)/(3)\pi r^2 h\\\\V =  \displaystyle(1)/(3)\pi r^2 (3r)\\\\3V = 3\pi r^3\\\\ r = \sqrt[3]{(3V)/(3\pi)}`