Suppose the curved surface area of a right circular cone is precisely equal to the area of its circular base. If the base radius is represented by r, determine the expression for its slant height l.

Correct Option: The correct option is r.

Step-by-Step Explanation:

1. Understand the given terms and formulas:

Let the base radius of the right circular cone be denoted by r, and its slant height be denoted by l.

The formula for the curved surface area (CSA) of a right circular cone is given by:

$\text{Curved Surface Area}=\pi rl$

The formula for the area of the circular base of the cone is given by:

$\text{Base Area}=\pi r^2$

2. Set up the equation according to the problem statement:

The problem states that the curved surface area of the cone is precisely equal to the area of its circular base.

Equating both expressions:

$\pi rl=\pi r^2$

3. Solve for the slant height l:

Divide both sides of the equation by $\pi r$ (since radius r > 0 and π ≠ 0):

$l=\frac{\pi r^2}{\pi r}$

Simplifying the fraction on the right-hand side:

$l=r$

Conclusion:

The expression for the slant height l is r.