Question

Find the missing measure for a right circular cone given the following information. Find V if r = 2 and L.A. = 12. (16/3)√2 16√2 4√(38)

Answer 1

The answer is (16/3)√2

Explanation:

I found the answer by following Netta00's awesome step by step.

Answer 2

Volume of cone is given by formula

`V = (\pi r^(2)h)/(3)`-------------------------------------------(1)

We are already given r =2, so we need to find h and then we can find volume

So missing meausre is height here ------------------------------------------------------------------------------

To find h we will use lateral area =
`12\pi` given

Formula for lateral area of cone is
`\pi r\sqrt{r^(2)+ h^(2)}`

so we have
`12 = \pi r\sqrt{r^(2)+ h^(2)}`

Now plug r as 2 in this equation

`12 \pi = \pi (2)\sqrt{2^(2)+ h^(2)}`

Now solve for h as shown and get h by itself

`(12\pi)/(2\pi) = \frac{2\pi\sqrt{4+h^(2)}}{2 \pi}`

`6 = \sqrt{4+h^(2)}`

`6^(2) = \sqrt{4+h^(2)} ^(2)`

`36} = 4+h^(2)`
`36 - 4 = 4+h^(2) -4`

`32 = h^(2)`
`√(32) = \sqrt{h^(2)}`

`√(16 * 2) = h`
`√(16) * √(2) = h`

`4√(2) = h`----------------------------------------------------(2)

Now plug 2 in r place and
`4√(2)` in h place in volume formula given in (1)

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

`V = (\pi (2)^(2)4√(2))/(3) [/tex</p><p>][tex] V = (\pi (4)4√(2))/(3)`

`V = (16 \pi √(2))/(3)`

so choice (1) is right answer

`(1) (16 √(2)\pi)/(3)`

correct answer --------------------------------------------------------------------------------------------------

`(2) 16 √(2) \pi`

incorrect answer as correct volume answer we got as
`(16 √(2)\pi)/(3)` --------------------------------------------------------------------------------------------------

`(3) 4 √(38) \pi`

incorrect answer as correct volume answer we got as
`(16 √(2)\pi)/(3)` --------------------------------------------------------------------------------------------------------