Find the missing dimension of a cone.

 

V = 566.77 m3, r = 9.5 m, h = Answer
5.997



To find the height \( h \) of the cone, we use the formula for the volume of a cone:

\[
V = \frac{1}{3} \pi r^2 h
\]

Given:
- \( V = 566.77 \, \text{m}^3 \)
- \( r = 9.5 \, \text{m} \)

Now, we can solve for \( h \):

\[
566.77 = \frac{1}{3} \pi (9.5)^2 h
\]

Simplifying the equation:

\[
566.77 = \frac{1}{3} \pi (90.25) h
\]

\[
566.77 = \frac{1}{3} \times 3.1416 \times 90.25 \times h
\]

Now solve for \( h \):

\[
566.77 = 94.67 h
\]

\[
h = \frac{566.77}{94.67} \approx 5.997 \, \text{m}
\]

Thus, the height \( h \) is approximately \( 5.997 \, \text{m} \).

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Would you like further details or have any questions?

Here are 5 related questions:
1. How would the volume change if the radius were doubled?
2. What is the surface area of this cone, including the base?
3. How does the volume of a cone compare to a cylinder with the same height and radius?
4. Can you derive the formula for the lateral surface area

Find the missing dimension of a cone. V = 566.77 m³, r = 9.5 m, h = ?

Learn how to find the missing height of a cone when given the volume of 566.77 m³ and a radius of 9.5 m. This geometry problem uses the formula V = (1/3) * π * r² * h and is ideal for students in Grades 9-12.

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