Answer:
V = 288.5 [tex]yd^{3}[/tex]
Step-by-step explanation:
To find the volume of a cone, use this equation:
[tex]V = \pi r^{2}\frac{h}{3}[/tex]
r = radius
h = height
We aren't given the height of the cone, just the length of the side. To find the height use the Pythagorean Theorem:
[tex]a^{2}+ b^{2}= c^{2}[/tex]
The value of 12.1 yds is the hypotenuse and the radius is the value of one of the legs. So, set it up like this:
[tex]a^{2}+5^{2} =12.1^{2}[/tex]
Now, solve:
[tex]a^{2}+25= 146.41[/tex] Distribute the square
[tex]a^{2} = 121.41[/tex] Subtract 25 from 146.41
[tex]\sqrt{a^{2} }=\sqrt{121.41}[/tex]
a = 11.01862
So, the height is equal to 11.01862 yds.
Now, we can plug everything into the volume equation:
[tex]V = \pi (5)^{2}\frac{11.01862}{3}[/tex]
Simplify (use calculator):
V = 288.5 [tex]yd^{3}[/tex]
So, the volume of the cone is equal to 288.5 [tex]yd^{3}[/tex]
