A right circular cone has a radius of 9 cm and a height of 40 cm. What is its slant height?

The correct option is 41 cm.

To find the slant height of a right circular cone when the radius and height are given, we use the Pythagorean theorem.

Given Data:
Radius of the cone (r) = 9 cm
Height of the cone (h) = 40 cm

Formula:
The relationship between the slant height (l), radius (r), and height (h) of a right circular cone is given by:

$l^2=r^2+h^2$

$l=\sqrt{r^2+h^2}$

Step-by-Step Calculation:

1. Substitute the given values of r and h into the formula:

$l=\sqrt{9^2+{40}^2}$

2. Calculate the squares of 9 and 40:

$9^2=81$

${40}^2=1600$

3. Add the squared values together:

$r^2+h^2=81+1600=1681$

4. Take the square root of the sum to find the slant height (l):

$l=\sqrt{1681}=41\text{cm}$

Thus, the slant height of the right circular cone is 41 cm.