Math  /  Geometry

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2400 square centimeters of material is available to make a box with a square base and an open top, find he largest possible volume of the box. olume = \square cubic centimeters. question Help: Video Submit Question

Studdy Solution
Verify the solution: - Calculate h h using x=202 x = 20\sqrt{2} :
h=2400(202)24(202) h = \frac{2400 - (20\sqrt{2})^2}{4(20\sqrt{2})} h=2400800802 h = \frac{2400 - 800}{80\sqrt{2}} h=1600802 h = \frac{1600}{80\sqrt{2}} h=202 h = \frac{20}{\sqrt{2}} h=102 h = 10\sqrt{2}
- Calculate the volume:
V=(202)2×102 V = (20\sqrt{2})^2 \times 10\sqrt{2} V=800×102 V = 800 \times 10\sqrt{2} V=80002 V = 8000\sqrt{2}
The largest possible volume of the box is:
80002 cubic centimeters \boxed{8000\sqrt{2}} \text{ cubic centimeters}

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