An object is shaped like an ice cream cone, consisting of a hemisphere placed on top of a cone with an identical base radius. The volume of the hemispherical part is 144π cm³, and the height of the conical part is 8 cm. What is the total surface area of the object?
Show answer & explanation
Correct answer: A
Explanation
Given:
Volume of the hemisphere = 144π cubic cm
Height of the cone = 8 cm
Formula:
Volume of the hemisphere = (2/3)πr³
Curved surface area of the cone = πrl
Curved surface area of the hemisphere = 2πr²
Total surface area = πrl + 2πr²
(2/3)πr³ = 144π
r³ = 216
r = 6 cm
Slant height of the cone
l = √(r² + h²)
= √(6² + 8²)
= √(36 + 64)
= √100
= 10 cm
Curved surface area of the cone = πrl
= π × 6 × 10
= 60π
Curved surface area of hemisphere= 2πr²= 2π × 36= 72π
Total surface area = 60π + 72π = 132π cm²