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22 September, 22:01

If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.

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  1. 22 September, 22:13
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    Let the sides of square base be "x" and height be "h" first come up with expressions for surface area and volume SA=2 x2 + 4hx=600 V=h x2 Next get h in terms of x and sub it into Volume equation h = 300 - x2 2x →V = (300 - x2 2x) x2 V=150x - 12 x3 maximize volume by setting derivative equal to 0 dV dx = 150 - 32 x2 = 0 solve for x x=10 which means h = 10 max volume occurs when box is a cube 10^3 = 1000 cm^3
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