Question

the volume of this cone is 30,464.28 cubic inches. what is the height of this cone? round your answer to the nearest hundredth. 21 in ( h approx ) inches

Explanation:

Step1: Recall cone volume formula

Volume \( V = \frac{1}{3}\pi r^2 h \)

Step2: Identify given values

\( V = 30464.28 \), \( r = 21 \), \( \pi \approx 3.14 \)

Step3: Rearrange for height \( h \)

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

Step4: Calculate denominator

\( \pi r^2 = 3.14 \times 21^2 = 3.14 \times 441 = 1384.74 \)

Step5: Compute numerator

\( 3V = 3 \times 30464.28 = 91392.84 \)

Step6: Find height

\( h = \frac{91392.84}{1384.74} = 66.0 \)

Answer:

66.00 inches