A Guide to Revising Area and Volume

MINDSET LEARN GRADE 11 MATHEMATICS

A Guide to Revising Area and Volume

Teaching Approach

Many learners tend to approach this section of Mathematics relying on memorising the formulae without understanding the concept of what a right prism is, what volume and surface area are, and the dimensions of cubic and square units that accompany these calculations respectively.

Formulae sheets are now provided for learners in assessments. However, learners still need to be able to identify which formula to use as the formulae will not be labelled. There will be a page of formulae on the formula sheet without necessary indicating whether specific formula are for volume or surface area and the particular prism they can be used for.

If learners can therefore identify a right prism and understand that for any right prism the

following formulae apply for volume and surface area, they will not need to memorise each

formula for each prism in order to recognise and select the correct formula.

Volume

= area of base x height of prism (at right angles to the base)

Surface area = 2 x area of base + perimeter of base x height of prism

Understanding these concepts (of volume and surface area) and the general formula for each will also better equip learners to deal with more complex and non-routine problems. In such problems a combination of figures are presented or learners are required to break a figure into smaller parts that are prisms they recognise.

The basic understanding of the general formulae for volume and surface area of right prisms and how to recognise a right prism has therefore been underpinned in the first video. Learners are also given a few examples of dealing with more complex figures and calculating the volume and surface area of prisms that are not right prisms. The skill of being able to recognise and match the correct prism with its corresponding formula has also been included in order to help prepare learners to effectively use the formulae sheets that will be provided in assessments.

These videos revise the skills covered in Grade 10. They can be watched in any sequence and as needed. The task video provides a comprehensive set of questions to test the viewers skills in this section.

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Video Summaries

Some videos have a `PAUSE' moment, at which point the teacher or learner can choose to pause the video and try to answer the question posed or calculate the answer to the problem under discussion. Once the video starts again, the answer to the question or the right answer to the calculation is given.

Mindset suggests a number of ways to use the video lessons. These include: Watch or show a lesson as an introduction to a lesson Watch of show a lesson after a lesson, as a summary or as a way of adding in some interesting real-life applications or practical aspects Design a worksheet or set of questions about one video lesson. Then ask learners to watch a video related to the lesson and to complete the worksheet or questions, either in groups or individually Worksheets and questions based on video lessons can be used as short assessments or exercises Ask learners to watch a particular video lesson for homework (in the school library or on the website, depending on how the material is available) as preparation for the next days lesson; if desired, learners can be given specific questions to answer in preparation for the next day's lesson

1. Revising Volume A right prism is first defined followed by an example of calculating the volume of a triangular prism using the general formula for calculating the volume of any right prism.

2. Revising Surface Area A general formula for calculating the surface area of right prisms is given as well as examples of how to apply this formula to various right prisms.

3. Revising Compound Solids This video focuses on calculating the surface area and volume of compound solids. It also looks at solids that are not right prisms.

Resource Material

1. Revising Volume

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This site is from the Department of Basic Education in South Africa and provides a summary of the formulae you need to know as well as a number of additional (easy and more difficult) examples that you can work through to practice calculating volume and surface area, especially of spheres, cones and pyramids and a combination of figures.

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2. Revising Surface Area 3. Revising Compound Solids

ss/surfaceareavol.htm

This site offers all the formulae for volume and surface area of right prisms, cones, pyramids and spheres that you need to know. It also has videos that you can watch that further explain these topics.

es/crossword/319

This is a fun site that generates crossword puzzles on various topics. For this video we selected the surface area and volume topic. You can check your knowledge of current and previous work on this by doing the puzzle and then checking your answers using the answer key. Try to do it all on your own first. Crosswords are also a great "mathematics brain exercise".

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Task

Question 1

1.1 Is this a right prism? Motivate your answer. 1.2 What shape is the base of this prism? Question 2

2.1 What is this object called? 2.2 Is it a right prism? Motivate your answer. 2.3 Here are four formulae. Select which formula is the correct one for calculating the

surface area of this object.

A) 1 r2h 3

B) 4 r2 C) r2 rs D) 2 r2 2 rh

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Question 3 Determine the volume of this prism if the following pattern is folded.

Question 4 Calculate the volume of swimming pool that has the following dimensions:

Length = 10 m Breadth = 4,2 m Depth = 1,2 m Question 5

5.1 Calculate the volume of this storage facility.

5.2 Calculate how many litres of paint you would need to paint this storage facility with one coat if one litre of paint covers approximately 15 m2.

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