The curved surface area of a right circular cone is 444π cm² and the diameter…

To find the volume of the right circular cone, we need to determine its radius, slant height, and vertical height.

Step-by-Step Calculation
Identify the Radius (r):
The base diameter is 24 cm, so the radius r = 24 / 2 = 12 cm.

Find the Slant Height (l):
The curved surface area of a cone is given by the formula A = π * r * l.
Given A = 444π cm²:
444π = π * 12 * l
l = 444 / 12
l = 37 cm

Calculate the Vertical Height (h):
In a right circular cone, the relationship between slant height (l), radius (r), and vertical height (h) is given by the Pythagorean theorem: l² = r² + h².
37² = 12² + h²
1369 = 144 + h²
h² = 1369 - 144
h² = 1225
h = √1225 = 35 cm

Calculate the Volume (V):
The formula for the volume of a cone is V = (1/3) * π * r² * h.
V = (1/3) * π * (12)² * 35
V = (1/3) * π * 144 * 35
V = π * 48 * 35
V = 1680π cm³