Aclosed box with a square base is to be built to house an ant colony. the bottom of the box and all four sides are to be made of material costing $1/ft², and the top is to be constructed of glass costing $5/ft². what are the dimensions of the box of greatest volume that can be constructed for $72?

Dimensions of the box will be 6 ft × 6 ft × 54 feet

Step-by-step explanation:

A closed box is to be built having square base.

Let the dimensions of the box are a ft × a ft × b ft.

Material used to build the base and all four sides cost $1 per square ft.

Therefore, cost of base and four sides = 1[(a)² + 4ab]

Top of the box is to be constructed of glass costing $5 per square feet.

Cost of the top = 5a²

Total cost of the box material = (a² + 4ab) + 5a² = $72

6a² + 4ab = 72

b = -----(1)

Now volume of the box V = a×a×b = a²b

From equation (1),

V = a²()

V = a(18 - 1.5a)

For greatest volume ,

18 - 3a = 0

a = 6

Now form equation (1)

b =

b = 54 feet.

Therefore, dimensions of the box will be 6 ft × 6 ft × 54 feet.

2,600 divided by 80 = 32.5

step-by-step explanation:

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.