Question

this was a question on my homework assignment from school but I don't know how to solve this without the height of the cone from top to bottom.

Answer 1

Answer:
`√(585)` units or
`3√(65)` units

Explanation:

The formula for volume of a cone is π
`r^(2)`
`(h)/(3)`. You can find the height by plugging in 72π for volume and 3 for radius.

diameter = radius x 2, so 6/2=3 units for radius.

72π = π(
`3^(2)`)(
`(h)/(3)`)

72=9*
`(h)/(3)`

8 =
`(h)/(3)`

h = 24 units

The formula for slant height is
`\sqrt{{r}^2 + {h}^2 }`

Plug in 3 for r and 24 for h. You should get
`√((9+576))`=
`√(585)` or 3
`√(65)` as your answer.