Question

the volume of this cone is 715.92 cubic centimeters. what is the height of this cone? round your answer to the nearest hundredth. 6 cm h ≈ centimeters submit

Explanation:

Step1: Recall cone volume formula

The volume \( V \) of a cone is \( V = \frac{1}{3}\pi r^2 h \), where \( r = 6 \, \text{cm} \) and \( V = 715.92 \, \text{cm}^3 \).

Step2: Rearrange for height \( h \)

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

Step3: Substitute values

\( h = \frac{3 \times 715.92}{\pi \times 6^2} = \frac{2147.76}{36\pi} \)

Step4: Calculate the value

Using \( \pi \approx 3.14 \):
\( 36\pi \approx 113.04 \), so \( h \approx \frac{2147.76}{113.04} \approx 19.00 \)

Answer:

19.00