Respuesta :
The smallest surface area of cubic rectangular boxes = 96 ft²
What is surface area?
An object with three dimensions is solid and has both height and depth. A sphere and a cube, for instance, have three dimensions, whereas a circle and a square do not.
A three-dimensional shape's total surface area equals the sum of its side's surface areas. The measured area of all surfaces of three-dimensional solids, such as cubes, spheres, prisms, and pyramids, is expressed in square units.
Since it is a closed rectangular box so, there will be two equal sides.
According to the given Information:
Volume = 64 ft³
Volume of rectangular cube = hx²
Surface area of rectangular cube = 2x²+4hx
Equating the above equation we get, hx² = 64
h=64/x²
Put the value of h in surface area formula,
S = 2x² + 4(64/x²)*x
S = 2x² + 256/x
For the surface area to be minimum,
ds/dx = 0
4x - (256/x²) = 0
4x³ = 256
x³ = 64
x = 4 ft
Therefore, the smallest surface area
= 2(4)² + (256/4)
S = 32 + 64
= 96 ft²
To know more about the surface area visit:
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