Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
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:
https://brainly.com/question/10604587
#SPJ4
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
