Answer:
184π units²
Explanation:
see attached for reference
given sloped height = 15 units
base radius = 8 units
the height of the cone can be found by using the Pythagorean equation
(sloped height)² = height ² + (base radius)²
15² = h² + 8²
h² = 15²-8² = 161
h = √161
Base surface area = πr² = π 8² = 64π units²
Lateral Surface Area,
= πr √(r² + h²)
= π(8) √[ (8)² + (√161)² ]
= 8π√(64 + 161)
= 8π√225
= 8π (15)
= 120π
Surface area = base area + lateral surface area
= 64π + 120π
= 184π units²