Answer:
To find the curved surface area of a cone, we need to know the height and the slant height (l) of the cone.
Given:
Height of the cone (h) = 15 cm
Volume of the cone = 320π cm³
The formula for the volume of a cone is given by:
Volume = (1/3) * π * r² * h
Explanation:
r = √[(3 * Volume) / (π * h)]
r = √[(3 * 320π) / (π * 15)]
r = √[960 / 15]
r = √64
r = 8 cm
Now, to calculate the slant height (l)
l = √(r² + h²)
l = √(8² + 15²)
l = √(64 + 225)
l = √289
l = 17 cm
calculate the curved surface area (CSA) using the formula:
CSA = π * r * l
CSA = π * 8 * 17
CSA = 136π cm²
Therefore, the curved surface area of the cone is 136π cm².