Ask Question
6 October, 15:08

A closed box with 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 $2/ft2, and the top is to be constructed of glass costing $4/ft2. what are the dimensions of the box of greatest volume that can be constructed for $72? (enter the dimensions (in feet) as a comma separated list.)

+5
Answers (1)
  1. 6 October, 15:17
    0
    Box has all sides same leinght (a). Area of that box is 6*a^2.

    Cost of material for bottom and 4 sides is 2$/ft^2. Area of bottom and sides is A=5*a^2

    Cost of material for top is 4$/ft^2. Area of top of the box is T=a^2

    A*2+T*4=72

    5*a^2*2+a^2*4=72

    a^2 * (10+4) = 72

    a^2*14=72, a^2=72/14, a=root (72/14), a=2.267ft

    Dimensions of the box: leinght of sides 2.2ft. Area of hole box 30.835ft^2

    Area of the bottom and sides: A=5*a^2=25.696ft^2

    Area of the top : T=a^2=5.139ft^2

    Check: A*2$+T*4$=71.95$
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A closed box with 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 ...” in 📗 Physics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers