# (iii) a closed top box with a square base will be made to hold 128 cubic feet. what are the dimensions that will minimize the surf

(iii) a closed top box with a square base will be made to hold 128 cubic feet. what are the dimensions that will minimize the surface area?

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1. The dimension that minimize the surface area is  side is 6.35 feet and height is 3.17 feet.

### What is volume?

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected. The space occupied inside an object’s borders in three dimensions is referred to as its volume. It is sometimes referred to as the object’s capacity. An object’s volume is the amount of space it occupies. Cubic meters are used to measure large quantities (m3). Cubic centimeters (cm3) or cubic millimeters are used to measure smaller quantities (mm3).
Here,
V=x²h
128=x²h
h=128/x²
A=x²+4xh
=x²+4x(128/x²)
=x²+512/x
A’=2x-512/x²
A’=(2x³-512)/x²
A’=0
2x³=512
x³=256
x=6.35 feet
h=128/(6.35)²
=3.174 feet
The side and height measurements that minimize the surface area are 6.35 feet and 3.17 feet, respectively.