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

Answer:

Volume of cone = 200.96 square feet              

Step-by-step 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.

$h = 3\times r = 3\times 4 = 12\text{ feet}$

Volume of tree =

$\text{Volume of cone} = \displaystyle\frac{1}{3}\pi r^2 h$

Putting all the values, we get,

$\text{Volume of tree} = \displaystyle\frac{1}{3}\pi (4)^2 (12)\\\\= \frac{1}{3}\times 3.14\times 4\times 4\times 12 = 200.96\text{ square feet}$

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

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