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marin [14]
3 years ago
15

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 tre

e 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)
Mathematics
1 answer:
german3 years ago
8 0

Answer:

Volume of Cone =

=  \frac{1}{3}\pi (2)^2 (4)\\\\=\frac{1}{3}(3.14)(4)(4)\\\\=\frac{1}{3}\times 3.14\times 16 \\\\=\frac{1}{3}\times50.24\\\\=16.746\\\\\approx16.75 \texttt {ft} ^3

Thus, Volume = 16.75 cubic feet

Step-by-step explanation:

Volume of a cone is given by the formula  

V=\frac{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 =

=  \frac{1}{3}\pi (2)^2 (4)\\\\=\frac{1}{3}(3.14)(4)(4)\\\\=\frac{1}{3}\times 3.14\times 16 \\\\=\frac{1}{3}\times50.24\\\\=16.746\\\\\approx16.75 \texttt {ft} ^3

Thus, Volume = 16.75 cubic feet

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