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A fish tank in the shape of a cuboid is to be made from 1600 cm of glass. The fish tank will have a square base of side length x cm, and no lid. No glass is wasted. The glass can be assumed to be very thin. (a) Show that the volume, V cm³, of the fish tank is given by V=400x (b) Given that x can vary, use differentiation to find the maximum or minimum value of V. (c) Justify that the value of V you found in part b is a maximum.

A fish tank in the shape of a cuboid is to be made from 1600 cm of glass. The fish tank will have a square base of side length x cm, and no lid. No glass is wasted. The glass can be assumed to be very thin. (a) Show that the volume, V cm³, of the fish tank is given by V=400x (b) Given that x can vary, use differentiation to find the maximum or minimum value of V. (c) Justify that the value of V you found in part b is a maximum.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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11. A fish tank in the shape of a cuboid is to be made from 1600 cmf of glass. The fish tank will have a square base of side length x cm, and no lid. No glass is wasted. The glass can be assumed to be very thin. (a) Show that the volume, V cm³, of the fish tank is given by V=400x* (b) Given that x can vary, use differentiation to find the maximum or minimum value of V. (c) Justify that the value of V you found in part b is a maximum.
Transcribed Image Text:11. A fish tank in the shape of a cuboid is to be made from 1600 cmf of glass. The fish tank will have a square base of side length x cm, and no lid. No glass is wasted. The glass can be assumed to be very thin. (a) Show that the volume, V cm³, of the fish tank is given by V=400x* (b) Given that x can vary, use differentiation to find the maximum or minimum value of V. (c) Justify that the value of V you found in part b is a maximum.
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