 # Differentiation: Maximum Volume

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How to find the maximum volume of a box?
Find the maximum volume of a box given a fixed surface area by considering stationary point.
Example:
Given an open box with area 486 cm2 and whose length is twice the width. Find the maximum volume. Show the volume is the max

A-Level Edexcel C2 June 2007 Q10(a)
Worked solution to this question on differentiation - maximum volume of a box
Figure 4 shows a solid brick in the shape of a cuboid measuring 2x cm by x cm by y cm.
The total surface area of the brick is 600 cm2.
(a) Show that the volume, V cm3, of the brick is given by
V = 200x - 4x3/3
Given that x can vary,
(b) use calculus to find the maximum value of V, giving your answer to the nearest cm3
(c) Justify that the value of V you have found is a maximum
A-Level Edexcel C2 June 2007 Q10(b)
Worked solution to this question on differentiation - maximum volume of a box. A-Level Edexcel C2 June 2007 Q10(c)
Worked solution to this question on differentiation - maximum volume of a box.

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