Question

Need to find the volume. measurements in picture, please help.​

Answer 1

V = 288.5
`yd^(3)`

Explanation:

To find the volume of a cone, use this equation:

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

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:

`a^(2)+ b^(2)= c^(2)`

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:

`a^(2)+5^(2) =12.1^(2)`

Now, solve:

`a^(2)+25= 146.41` Distribute the square

`a^(2) = 121.41` Subtract 25 from 146.41

`\sqrt{a^(2) }=√(121.41)`

a = 11.01862

So, the height is equal to 11.01862 yds.

Now, we can plug everything into the volume equation:

`V = \pi (5)^(2)(11.01862)/(3)`

Simplify (use calculator):

V = 288.5
`yd^(3)`

So, the volume of the cone is equal to 288.5
`yd^(3)`