Geometry

Question Analysis:
This problem requires deriving volume from surface area by first calculating slant height, then perpendicular height.

Key Concept Explanation:
Surface Area Components:
Base Area (square) = side²
Lateral Area = (perimeter × slant height)/2
Volume Formula: V = (1/3) × base area × perpendicular height
Height Relationship: Pythagorean theorem connects slant height (l) and perpendicular height (h): 

Step-by-Step Solution:
Calculate Base Area:
6 cm × 6 cm = 36 cm²
Determine Lateral Area:
Total SA - Base Area = 108 - 36 = 72 cm²
Find Slant Height (l):
Lateral Area = (perimeter × slant height)/2
72 = (24 × l)/2 → l = 6 cm
Calculate Perpendicular Height (h):

Click "Show Answer" to reveal the answer and analysis