Question

How do you solve this?

Answer 1

`100\pi \text{ in}^3`

Explanation:

Volume of a Cone Equation:

`v = (1)/(3)* \pi * r^2 * h`

1) Find h

Use the Pythagorean Theorem to find h

`a^2 * b^2 = c^2`

Change diameter to radius. (10 in ---> 5in)

a = 5

`1) 5^2 + b^2 = 13^2\\\\2) 25 + b^2 = 169\\\\3) b^2 =144\\\\4) 12`

Step 2) Subtract 25 on both sides so
`b^2` is alone

Step 3) Square root both sides

Step 4) h = 12

2) Plug in known variables:

h = 12 in

r = 5 in;

Equation now:

`v = (1)/(3) * \pi * 5^2 * 12`

3) Solve:

`1) (1)/(3) * \pi * 5^2 * 12\\\\2) (\pi)/(3) * 5^2 * 12\\\\3) (\pi)/(3) * 25 * 12 \\\\4) (\pi)/(3) * 300\\\\5) (300\pi)/(3) \\\\\text{Simplify:}\\100\pi`