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Grade 9

Algebra and geometry

Module 7

Space and shape

Activity 1:

To understand the structure of some regular right prisms

[LO 3.3, 3.4]

A. Building cont a iners

You will be given a sheet of shapes. You will need a ruler that you can measure with, a pair of scissors and glue or sticky tape. Colouring pens will also be helpful. Do the following with these shapes:

  1. Carefully measure all the lines and write down your measurements ( you should be able to measure to the nearest half–millimetre). You must also do your best to measure the radius (or diameter) of the circle. If you have a protractor available, find out where the 90°–angles are.
  2. Using these measurements, calculate the areas of the different shapes, and add the parts together to find out the total area of each of the four shapes. Set your work out very clearly so that anybody can understand what you have done. Use the proper names for the shapes you describe.

For example, for the last figure you could say:

Total area = small rectangle + small rectangle + large rectangle

= ( l × b ) + ( l × b ) + ( l × b )

and so on . . . (Remember to use appropriate units.)

  1. Very carefully cut out the given shapes. You can colour these shapes to make it easier to see which the top and base are, and which the sides (the sides are striped). Now fold them and use tape, or glue and paper strips, to make four boxes. Keep the sides with the dotted lines on the outside.
  2. Write down what the Total Surface Area (TSA) of each shape is. (You have already calculated the answer!)
  3. Work in groups of two or three to try to find out how many 1cm × 1cm blocks will fit into each box. This is called the volume of the box. If you can find a method or a formula that will work with each of the four shapes, write that down carefully.
  4. At the end of this exercise, you should have two formulas.

B. Right prisms

  • Each of the four boxes is a right prism . These are shapes with a top and base that are exactly the same size and shape, and sides that go up straight at right angles to the base. Look around to see whether you can discover shapes with these characteristics.
  • We name right prisms according to the shape of the base, e.g. square prism, rectangular prism, triangular prism and circular prism (cylinder).
  • Are these two shapes right prisms? Describe the shape of the base of each, and confirm whether the sides go straight up at right angles to the base.
  • What kind of work did you do in this section? Score yourself in this table.
Did i work Excellent Adequately Not well enough
well with my team?
according to instructions?

C. Formul a s

  • To calculate the total surface area (TSA) and volume (V) of any right prism we use the following general formulas: (Please note that H refers to the prism height.)

TSA = 2 × base area + sides area and V = base area × prism height

Here are some important e x amples. These are the cut–out prisms you made into boxes. Please note how each part of the calculation is done separately and then put into the formula at the end.

  1. Squ a re prism :

Questions & Answers

Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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