Question

1. what’s the height of a cone if the volume is 562 cubic inches and the radius is 5 inches. what’s the height of a cone if the volume is 562 cubic inches and the radius is 5 inches. 72.05 units 21.48 units 120.62 units 38.90 units

Explanation:

Step1: Recall Cone Volume Formula

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step2: Rearrange Formula for \( h \)

We need to solve for \( h \), so rearrange the formula:
\( h = \frac{3V}{\pi r^2} \)

Step3: Substitute Values

Given \( V = 562 \) cubic inches and \( r = 5 \) inches. Substitute into the formula:
\( h = \frac{3 \times 562}{\pi \times 5^2} \)

Step4: Calculate Numerator and Denominator

First, calculate the numerator: \( 3 \times 562 = 1686 \)
Then, calculate the denominator: \( \pi \times 25 \approx 3.1416 \times 25 = 78.54 \)
Now, divide: \( h \approx \frac{1686}{78.54} \approx 21.48 \)

Answer:

21.48 units