The volume of this cone is 75.36 cubic meters. What is the height of this cone?

Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

3 m

h ≈
meters



Answer :

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.