# Exam Style Question

## Worked solutions to typical exam type questions that you can reveal gradually

##### List Of QuestionsExam Style QuestionMore Differentiation QuestionsOther Topics

Question id: 104. This question is similar to one that appeared in an IB Studies paper in 2014. The use of a calculator is allowed.

### Differentiation Optimisation

A child's play tent is made in the shape of half a cylinder. It is constructed from a fibreglass frame with material pulled tightly around it. The fibreglass frame consists of a rectangular base, two semi-circular ends and two further support rods, as shown in the following diagram.

The semicircular ends each have radius $$r$$ and the support rods each have length $$d$$.

Let F be the total length of fibreglass used in the frame of the play tent.

(a) Write down an expression for $$F$$ in terms of $$r$$, $$d$$ and $$\pi$$.

The volume of the play tent is 0.95 m3.

(b) Write down an equation for the volume of the play tent in terms of $$r$$, $$d$$ and $$\pi$$.

(c) Show that $$F = 2\pi r + 4r + \frac{7.6}{\pi r^2}$$

(d) Find $$\frac{dF}{dr}$$

The play tent is designed so that the length of fibreglass used in its frame is a minimum.

(e) Find the value of $$r$$ for which $$F$$ is a minimum.

(f) Calculate the value of $$d$$ for which $$F$$ is a minimum.

(g) Calculate the minimum value of $$F$$.

 The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.

Drag this panel down to reveal the solution

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.

## Comments:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For All:

©1997-2018 WWW.TRANSUM.ORG

©1997 - 2018 Transum Mathematics :: For more exam type questions and worked solutions go to Transum.org/Maths/Exam/