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.
More Lessons for A Level Maths
Math Worksheets
A collection of videos, activities and worksheets that are suitable for A Level Maths.
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
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
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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