Algebra-1

Question Analysis
This question tests the ability to apply the Product of Powers Rule in the context of geometric shapes, specifically a cylinder. It requires understanding how to use exponents to express and simplify the volume and surface area.

Key Concept Explanation
The Product of Powers Rule states that when multiplying two or more powers with the same base, you add their exponents. For any non-zero number and integers , , .

Step-by-step Solution
1. Simplify the dimension relationship (height = 9×width):
Since , substitute and : →
2. Equate the exponents: . (Equation 1).
3. Simplify the volume equation ( ):
Substitute the given values: .
4. Equate the exponents: . (Equation 2)
5. Simplify the base area equation (