Determine the Dimensions of a Rectangular Solid (With a Square $\frac { 20 \sqrt { 6 } } { 3 }$

question 73

Multiple Choice

Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 400 square meters.

• A)square base side \(\frac { 20 \sqrt { 6 } } { 3 }\) ; height \(\frac { 20 \sqrt { 6 } } { 3 }\)
• B)square base side \(\frac { 20 \sqrt { 6 } } { 3 }\) ; height \(\frac { 10 \sqrt { 6 } } { 3 }\)
• C)square base side \(\frac { 10 \sqrt { 6 } } { 3 }\) ; height \(\frac { 20 \sqrt { 6 } } { 3 }\)
• D)square base side \(\frac { 10 \sqrt { 6 } } { 3 }\) ; height \(\frac { 10 \sqrt { 6 } } { 3 }\)
• E)square base side \(\frac { 200 \sqrt { 6 } } { 3 }\) ; height \(\frac { 10 \sqrt { 6 } } { 3 }\)

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Definitions:

High-Income

Relating to individuals, households, or countries with significantly higher earnings or GDP per capita compared to the average.

World Bank

A worldwide financial entity providing lending and grants to underdeveloped countries' governments for capital project development.

Real Output

The total value of all goods and services produced in an economy, adjusted for inflation, reflecting the actual productivity.

Per Capita

A statistical measure that divides an aggregate by the number of individuals in a population to give an average.