Question

What is the length of the radius?

Answer 1

Given:

`\bullet \ \ \text{Volume of party hat} = 75\pi \text{ inches}^(3)`

`\bullet \ \ \text{Radius of party hat:}\ 5 \ \text{inches}`

Recall that the formula to find the volume of a cone is πr²h/3. Now, let's use the formula to find the height.

`\bullet \rightarrow \text{Volume of cone:} \ ( \pi r^(2) h)/(3)`

`\bullet \rightarrow \text{Volume of party hat} =( \pi r^(2) h)/(3) = 75\pi \text{ inches}^(3)`

`\bullet \rightarrow ( (\pi )( 5^(2))( h))/(3) = 75\pi \text{ inches}^(3)`

`\bullet \rightarrow (\pi )( 5^(2))( h)} = 75\pi * 3`

`\bullet \rightarrow { (\pi )( 25)( h)}= 225\pi`

`\bullet \rightarrow \frac{{ (\pi )( 25)( h)}}{25} = (225\pi)/(25)`

`\bullet \rightarrow { (\pi )( h)}= 9\pi`

`\bullet \rightarrow \frac{{ (\pi )( h)}}{\pi } =( 9\pi)/(\pi )`

`\bullet \rightarrow \boxed{\bold{h= 9 \ \text{inches}}}`

Thus, the height of the party hat is 9 inches.

Answer 2

h is 9 inches

Explanation:

the volume of the cone is 2π
`r^(2)`(h)(1/3）

just substitution, easy

75π=2π
`r^(2)`(h)(1/3）