Solve the Problem $x$ Height $y \mathrm {~cm}$ the Box's Surface Area Is Given By a Square

question 226

Multiple Choice

Solve the problem.
-An open-top rectangular box has a square base and it will hold 256 cubic centimeters (cc) . Each side has length $x$ height $y \mathrm {~cm}$ . The box's surface area is given by
$$S ( x ) = \frac { 1024 } { x } + x ^ { 2 }$$
Estimate the minimum surface area and the value of $x$ that will yield it.

• A) \(256 \mathrm {~cm} ^ { 2 }\) when \(x = 6 \mathrm {~cm}\)
• B) \(256 \mathrm {~cm} ^ { 2 }\) when \(x = 8 \mathrm {~cm}\)
• C) \(192 \mathrm {~cm} ^ { 2 }\) when \(x = 8 \mathrm {~cm}\)
• D) \(108 \mathrm {~cm} ^ { 2 }\) when \(x = 8 \mathrm {~cm}\)

---

Definitions:

Substitution Effect

A principle describing how changes in relative prices can lead consumers to substitute one good for another more or less expensive one, affecting demand levels.

Nike Soccer Balls

These are soccer balls produced and branded by Nike, a multinational corporation known for its wide range of sports equipment, apparel, and accessories.

Adidas Soccer Balls

Branded sports equipment produced by Adidas, specifically designed for playing soccer.

Demand and Supply

Fundamental economic concepts that describe the relationship between the quantity of a commodity that consumers wish to buy at various prices (demand) and the quantity that producers are willing to sell (supply).