The Volume of a Cylinder Whose Height Is Equal to Twice

question 253

Multiple Choice

The volume of a cylinder whose height is equal to twice its radius is $\mathrm { f } ( \mathrm { x } ) = 2 \pi \mathrm { x } ^ { 3 } \mathrm {~cm} ^ { 3 }$ , where x is the radius of the cylinder in cm . Find the inverse of this function.

• A) \(f ^ { - 1 } ( x ) = 2 \pi \sqrt [ 3 ] { x }\)
• B) \(f ^ { - 1 } ( x ) = \frac { 1 } { 2 \pi x ^ { 3 } }\)
• C) \(f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x } { 2 \pi } }\)
• D) \(f ^ { - 1 } ( x ) = \frac { \sqrt [ 3 ] { x } } { 2 \pi }\)

---

Definitions:

Position Equation

A mathematical equation that describes an object's position in terms of time and other variables, often used in physics.

Distance

The length of the shortest path between two points, often measured in units such as meters or miles.

System Of Linear Equations

A set of equations with two or more variables where each equation is linear.

Augmented Matrix

A matrix obtained by appending the columns of two given matrices, typically representing a system of linear equations.