Question

If 300 cm^2 of material is available to make a box with a square base and an open 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.

Answer 1

Hello,
Assume a the side of the base, b the height.


`V=a^2*b\\ a^2+4ab=300==\ \textgreater \ b= (300-a^2)/(4a) \\ V=a^2*(300-a^2)/(4a)= (1)/(4) *(300a-a^3)\\ (dV)/(da) = (1)/(4) *(300-3*a^2)=0\\ ==\ \textgreater \ a=10 \ and\ b=5\\ V=10^2*5=500\\`