The table shows the volume of two similar solids, right circular cylinder and right circular cylinder . The radius of right circular cylinder is units. The surface area of cylinder is square units, and the surface area of cylinder is square units, where and are constants. What is the value of ? (The surface area of a right circular cylinder with radius and height is .)
Enter a number or fraction, e.g. 5, 0.5, 1/2
Explanation
Question Type: Similar Solids
💡 Trick: For similar solids: if volume ratio = k³, then surface area ratio = k²
Solution:
- Volume ratio: 4000π/32π = 125 = 5³
- Scale factor k = 5
- Cylinder A: r = 4, V = 32π → πr²h = 32π → h = 2
- Surface area A = 2πr² + 2πrh = 2π(16) + 2π(4)(2) = 32π + 16π = 48π
- So k = 48
- Surface area ratio = 5² = 25
- Surface area B = 48π × 25 = 1200π
- So n = 1200
- n - k = 1200 - 48 = 1152
Answer: 1152