Maximum/minimum Cylinder

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Maria Aneiros 5 years, 10 months ago

Created this as a copy of Maximum/minimum2.

Name	Status	Author	Last Modified
Maximum/minimum2	draft	Frank Doheny	18/11/2016 11:37
Simon's copy of Maximum/minimum2	draft	Simon Thomas	14/03/2019 09:54
Simon's copy of Simon's copy of Maximum/minimum2	draft	Simon Thomas	14/03/2019 11:15
Maximum/minimum Cylinder	draft	Maria Aneiros	17/11/2020 11:43

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Question statement

A closed cylindrical tank is to be built having a volume of $\var{v}$ cm³.

Determine the required height, $h$ , and radius, $r$ , if the total surface area is to be a minimum.

Give any introductory information the student needs.

			Name	Type	Generated Value

integer

200

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Generated value: `integer`

200

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Parts

Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Input the cyinder height, correct to two decimal places.

$h =$ Gap 0.

Input the required cylinder radius, correct to two decimal places.

$r =$ Gap 1.

Advice

$\pi r^2h=\var{v}$

$h=\frac{\var{v}}{\pi r^2}$

The total surface area is to be a minimum.

Lid + curved surface area + base

$A=\pi r^2+2\pi rh+\pi r^2$

$A=2\pi r^2+2\pi r\left(\frac{\var{v}}{\pi r^2}\right)$

$A=2\pi r^2+\simplify{2*{v}}r^{-1}$

$\frac{dA}{dr}=4\pi r-\simplify{2{v}}r^{-2}=0$

$4\pi r=\simplify{2*{v}}/{r^2}$

$r^3=\frac{\var{v}}{2\pi}$

$r=\simplify{({v}/(2*pi))^(1/3)}$

From the second line we have the relation $h=\frac{\var{v}}{\pi r^2}$ to get

$h=2*\simplify{({v}/(2*pi))^(1/3)}$

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Taxonomy: mathcentre

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Maria Aneiros 5 years, 10 months ago

Error in variable testing condition

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Generated value: `integer`

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Maximum/minimum Cylinder

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Maria Aneiros 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`