# Exam-Style Question on Optimisation

## A mathematics exam-style question with a worked solution that can be revealed gradually

##### List Of QuestionsExam-Style QuestionMore Optimisation QuestionsMore on this Topic

Question id: 452. This question is similar to one that appeared on an A-Level paper (specimen) for 2017. The use of a calculator is allowed.

Moresum Soup is sold in cans with a capacities of 400ml each. Each can is in the shape of a right circular cylinder with radius $$r$$ cm and height $$h$$ cm.

(a) Assuming that the can is made from a metal of negligible thickness prove that the total surface area, A cm2, of the can is given by the following formula:

$$A= 2 \pi r^2 + \frac{800}{r}$$

(b) Given that r can vary, find the dimensions of a can that has minimum surface area.

 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

If you need more practice try the self-checking interactive exercises called Differentiation.

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.