2 Answers

Skyler Saleh · Answer 1 · 2023-09-29T23:37:02+0000

Solution:

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.

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