Single correct option
A right circular cone is hollowed out of a solid right circular cylinder of radius 6 cm and height 8 cm. The cone has the same base and height as the cylinder, and its base coincides with the bottom face of the cylinder. What is the total surface area of the remaining solid?
- A. 228π cm²
- B. 156π cm²
- C. 168π cm²
- D. 192π cm²
Show answer and solution
Answer: (D) 192π cm²
The remaining solid's surface consists of three parts:
1. Curved surface of the cylinder = 2πrh = 2π × 6 × 8 = 96π.
2. The top face of the cylinder (still intact) = πr² = 36π.
3. The inner curved surface of the conical cavity = πrl, where l = √(6² + 8²) = 10, so 60π.
The bottom face is removed (it is the base of the cavity).
Total = 96π + 36π + 60π = 192π cm².
Trap: 228π counts the bottom face too; 156π omits the top.
1. Curved surface of the cylinder = 2πrh = 2π × 6 × 8 = 96π.
2. The top face of the cylinder (still intact) = πr² = 36π.
3. The inner curved surface of the conical cavity = πrl, where l = √(6² + 8²) = 10, so 60π.
The bottom face is removed (it is the base of the cavity).
Total = 96π + 36π + 60π = 192π cm².
Trap: 228π counts the bottom face too; 156π omits the top.
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