Answer:
To find the height of the cone, we use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Given:
- \( V = 75.36 \) cubic meters
- \( \pi \approx 3.14 \)
- \( r = 3 \) meters
We need to solve for \( h \):
\[ 75.36 = \frac{1}{3} \times 3.14 \times (3^2) \times h \]
First, calculate \( 3^2 \):
\[ 3^2 = 9 \]
Now substitute and simplify:
\[ 75.36 = \frac{1}{3} \times 3.14 \times 9 \times h \]
\[ 75.36 = \frac{1}{3} \times 28.26 \times h \]
\[ 75.36 = 9.42h \]
To find \( h \), divide both sides by 9.42:
\[ h = \frac{75.36}{9.42} \]
\[ h \approx 8.00 \]
So, the height of the cone is approximately 8.00 meters.
