the volume of this cone is 17,662.5 cubic centimeters. what is the height of this cone? round your answer to…

Explanation:

Step1: Recall cone volume formula

The volume ( V ) of a cone is ( V = \frac{1}{3}\pi r^2 h ), where ( r = 25 , \text{cm} ), ( V = 17662.5 , \text{cm}^3 ).

Step2: Rearrange to solve for ( h )

Rearrange formula: ( h = \frac{3V}{\pi r^2} )

Step3: Substitute given values

Substitute ( V=17662.5 ), ( r=25 ): ( h = \frac{3 \times 17662.5}{\pi \times 25^2} )

Step4: Calculate denominator and numerator

First compute numerator: ( 3 \times 17662.5 = 52987.5 ) Denominator: ( \pi \times 625 \approx 1963.495 )

Step5: Compute final height

( h \approx \frac{52987.5}{1963.495} \approx 27.0 )

Answer:

( h \approx 27.00 ) centimeters