The radius of a solid right circular cone is 24 cm and its height is 32 cm. The total surface area of the cone is:

The correct answer is 960π cm².

To find the surface area of the solid right circular cone, we first need to determine its slant height using the given radius and height.

Step 1: Identify the given dimensions
Radius of the cone (r) = 24 cm
Height of the cone (h) = 32 cm

Step 2: Calculate the slant height (l)
The slant height of a right circular cone is given by the Pythagorean theorem:
$l=\sqrt{r^2+h^2}$
Substituting the given values:
$l=\sqrt{{24}^2+{32}^2}$
$l=\sqrt{576+1024}$
$l=\sqrt{1600}$
$l=40\text{cm}$

Step 3: Calculate the curved (lateral) surface area
The curved surface area (CSA) of a cone is given by the formula:
$\text{CSA}=\pi rl$
Substituting the values of the radius and the calculated slant height:
$\text{CSA}=\pi \cdot 24\cdot 40$
$\text{CSA}=960\pi {\text{cm}}^2$
Thus, the curved surface area corresponding to the correct option is 960π cm².