Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Answer:
Volume = [tex]7969[/tex] cubic centimeter
Step-by-step explanation:
Let the length of each side of the base of the box be A and the height of the box be H.
Area of material required to make the box is equal to is [tex]A^2 + 4*A*H.[/tex]
[tex]A^2 + 4*A*H = 1900[/tex]
Rearranging the above equation, we get -
[tex]`H = \frac{(1900 - A^2)}{(4*A)}[/tex]
Volume of box is equal to product of base area of box and the height of the box -
[tex]V = A*A* H[/tex]
Substituting the given area we get -
[tex]\frac{A^2*(1900 - A^2)}{4A} = \frac{(1900*A - A^3)}{4}[/tex]
For maximum volume
[tex]\frac{dV}{dA} =0[/tex]
[tex]\frac{ 1900}{4} - \frac{3*A^2}{4} = 0[/tex]
[tex]A^2 = \frac{1900}{3}[/tex]
Volume of the box
= [tex]\frac{\frac{1900}{3}*(1900 - \frac{1900}{3}) }{4 * \sqrt{\frac{1900}{3} } }[/tex]
= [tex]7969[/tex] cubic centimeter
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
