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More Lessons for A Level Maths

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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 cm^{2} 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 cm^{2}.

(a) Show that the volume, V cm^{3}, of the brick is given by

V = 200x - 4x^{3}/3

Given that x can vary,

(b) use calculus to find the maximum value of V, giving your answer to the nearest cm^{3}

(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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for A Level Maths

Math Worksheets

A collection of videos, activities and worksheets that are suitable for A Level Maths.

Find the maximum volume of a box given a fixed surface area by considering stationary point.

Example:

Given an open box with area 486 cm

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 cm

(a) Show that the volume, V cm

V = 200x - 4x

Given that x can vary,

(b) use calculus to find the maximum value of V, giving your answer to the nearest cm

(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.

Worked solution to this question on differentiation - maximum volume of a box.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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