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:

Markup

The amount added to the cost price of goods to cover overhead and profit; it calculates the selling price.

Manufacturing Overhead

All indirect costs associated with manufacturing, excluding direct materials and direct labor, such as maintenance, depreciation, and utilities.

Predetermined Overhead Rate

A rate calculated before a period begins, based on the estimated total manufacturing overhead costs and estimated allocation base, used to allocate overhead to products or job orders.

Manufacturing Departments

Specialized sections within a manufacturing facility responsible for different stages of product production, such as assembly, finishing, or quality control.