https://file.aiquickdraw.com/mathbot/file/1726524978837k6dwinvu.jpg

The question from the image reads (translated from Indonesian):

"It is known that the diameter of a cone is 14 cm, and its slant height is 25 cm. The volume of the cone is ..."

To solve this, we need to use the formula for the volume of a cone:

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

Where:
- \( r \) is the radius of the cone's base,
- \( h \) is the height of the cone (not the slant height).

We are given the diameter (14 cm), so the radius \( r \) is:

\[
r = \frac{14}{2} = 7 \, \text{cm}
\]

To find the height \( h \), we use the Pythagorean theorem, as the slant height (25 cm) forms the hypotenuse of a right triangle with the height and the radius:

\[
h^2 + r^2 = \text{slant height}^2
\]

Let's calculate the height and then the volume of the cone.The volume of the cone is approximately \( 1231.5 \, \text{cm}^3 \). This matches option A, which is \( 1232 \, \text{cm}^3 \).

Would you like more details or further clarification on the solution?

Here are five related questions:
1. How do you calculate the surface area of a cone?
2. What is the difference between slant height and height in a cone?
3. How does changing the diameter of the cone affect its volume?
4. Can you derive the volume formula for a cone?
5. How does the volume of a cone compare to the volume of a cylinder with the same base and height?

**Tip**: When dealing with cones, always ensure you distinguish between the slant height and the perpendicular height before applying volume or surface area formulas.

Diketahui diameter sebuah kerucut 14 cm dan garis pelukisnya 25 cm. Volume kerucut tersebut adalah ...

Find the volume of a cone with a diameter of 14 cm and a slant height of 25 cm using the volume formula and Pythagorean theorem. Detailed solution with step-by-step calculations for students in Grades 8-10.

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