The image shows a cone with a slant height of 74 cm, and you are tasked with finding the radius $r$ of the cone. The given curved surface area of the cone is $1776\pi$ cm². The formula for the curved surface area of a cone is:

$\text{Curved Surface Area} = \pi r l$

where:

• $r$ is the radius,
• $l$ is the slant height.

Step-by-Step Solution:

We are given:

• Slant height $l = 74 \, \text{cm}$,
• Curved surface area $1776\pi \, \text{cm}^2$.

The formula becomes:

$1776\pi = \pi r \times 74$

We can cancel $\pi$ from both sides:

$1776 = 74r$

Now, solve for $r$:

$r = \frac{1776}{74} = 24 \, \text{cm}$

Final Answer:

The radius $r$ of the cone is 24 cm.

Would you like more details on this, or have any further questions?

Related Questions:

1. What is the total surface area of the cone, including the base?
2. How do you find the volume of the cone given the radius and height?
3. If the height of the cone is required, how would you find it using the radius and slant height?
4. How does changing the slant height affect the surface area of a cone?
5. Can the same formula for the surface area be applied to other conical shapes?

Tip:

When solving problems involving cones, always distinguish between slant height and perpendicular height, as each plays a role in different calculations (surface area vs. volume).