A Box Is Created from a Square Piece of Cardboard $V = 4 x ^ { 3 } - 64 x ^ { 2 } + 256 x$

question 113

Multiple Choice

A box is created from a square piece of cardboard with sides measuring s = 16 cm by cutting a square from each corner and folding up the sides. Let x represent the length of the sides of the squares Removed from each corner.
Find an expression representing the volume of the box.

• A) \(V = 4 x ^ { 3 } - 64 x ^ { 2 } + 256 x\)
• B) \(V = x ^ { 3 } - 64 x ^ { 2 } + 1024 x\)
• C) \(V = x ^ { 3 } - 32 x ^ { 2 } + 256 x\)
• D) \(V = 16 x ^ { 2 } + 4 x ^ { 3 }\)

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Definitions:

Per Capita Real Income

The average income earned per person in a given area, adjusted for inflation, reflecting the true purchasing power of the populace.

Percent Per Year

A rate that expresses the change of a quantity over one year as a percentage of the initial quantity.

Productivity

A measure of the efficiency with which goods and services are produced, often expressed as output per unit of labor.

Real GDP Per-Person

A measure of a country's economic output that accounts for population size, providing an average economic output per individual, adjusted for inflation.