Question

the volume of this cone is 363,772.14 cubic millimeters. what is the height of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 69 mm h ≈ \boxed{} millimeters submit

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height. We know \( V = 363772.14 \) cubic millimeters, \( \pi \approx 3.14 \), and \( r = 69 \) millimeters. We need to solve for \( h \).

First, rearrange the formula to solve for \( h \):
\[
h = \frac{3V}{\pi r^2}
\]

Step2: Substitute the known values into the formula

Substitute \( V = 363772.14 \), \( \pi = 3.14 \), and \( r = 69 \) into the formula for \( h \):

First, calculate \( r^2 \):
\( r^2 = 69^2 = 4761 \)

Then, calculate \( \pi r^2 \):
\( 3.14 \times 4761 = 3.14 \times 4761 = 14949.54 \)

Next, calculate \( 3V \):
\( 3 \times 363772.14 = 1091316.42 \)

Now, divide \( 3V \) by \( \pi r^2 \) to find \( h \):
\[
h = \frac{1091316.42}{14949.54}
\]

Step3: Perform the division

Calculate the division:
\( \frac{1091316.42}{14949.54} \approx 73.0 \) (Wait, let's do the division more accurately. Let's compute \( 1091316.42 \div 14949.54 \))

\( 1091316.42 \div 14949.54 = \frac{1091316.42}{14949.54} \)

Let's divide numerator and denominator by 14949.54:

\( 1091316.42 \div 14949.54 = 73.0 \)? Wait, let's check:

\( 14949.54 \times 73 = 14949.54 \times 70 + 14949.54 \times 3 = 1046467.8 + 44848.62 = 1091316.42 \). Oh, so it's exactly 73.0.

Answer:

\( 73.00 \) (rounded to the nearest hundredth)