# 3.1 The volume and exterior surface of prisms

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## The volume and exterior surface area of prisms

ACTIVITY 1

Discovering the volume and exterior surface area of prisms and formulating a formula for calculating this, and applying the discovered formulas in practical situations

[LO 3.8, 4.2, 4.3, 4.5]

• Information that could be useful while executing this investigation should be noted down here. Your educator will assist you to ensure that the information is correct before you commence the investigation.

1. Write the formulas for calculating the area and volume of each of the following figures:

1.1 Area of a square:

1.2 Area of a rectangle:

1.3 Area of a triangle:

1.4 Area of a circle:

1.5 Volume of a rectangular prism:

1.6 Volume of a cylinder:

2. Explain what you understand the following to be and sketch it.

2.1 rectangular prism:

Sketch:

2.2 triangular prism:

Sketch:

2.3 cube:

Sketch:

2.4 cylinder:

Sketch:

3. What do you understand by the word “volume”?

4. Name the standard unit of measurement for each of the following:

• volume:
• water in a dam, cool drink in bottle:

5. Study the following representations of nets.

5.1 Rectangular prism:

5.2 Triangular prism (this is not a proper pyramid):

HOMEWORK ASSIGNMENT

Date of submission:

1. Collect the following sweet containers: a rectangular prism, a triangular prism, a cube and a cylinder. Unfold each example so that the complete area is visible and paste each onto a separate sheet of cardboard.

2. Draw a net to represent each of the figures. Indicate the lengths of the sides.

3. Make use of your existing knowledge and determine the total surface area and volume of each example.

4. Work out a formula for calculating the total surface area and the volume of each figure. You may refer to sources for help.

1. Collect other prisms found in everyday situations and calculate the total surface area. (One example will do)

ASSESSMENT RUBRIC: INVESTIGATION

 Criterion 1: The net is constructed accurately. (CONSTRUCTION) Criterion 2: The surface areas and volumes are calculated correctly. (CALCULATIONS) Criterion 3: The deduction of formulas for surface areas and volumes is correct. (FORMULAS) Criterion 4: The application in practical situations is correct. (REPORT)
 CRITERION NOT ACHIEVED AVERAGE ACHIEVEMENT ACHIEVED EXCEPTIONAL MARKS Construction The nets are not well constructed. The nets are constructed relatively well. The nets are constructed well. The nets are constructed to meet the requirements for a perfect net. /20 Calculations The calculations are incorrect. The calculations are partially correct. The calculations are (70 – 90%) correct. The calculations are (100%) correct. /10 Formulas The formulas are not correct or mathematical. The formulas are partially correct and mathematical. The formulas are 99% correct. The formulas are 100% correctly presented. /10 Report The report is untidy. The applications (use of mathematics) is weak. The report is fairly good, but the application is not altogether correct in every instance. The report is well-presented and the application is correct. The manner of presentation reveals that extra effort has gone into the exercise. /10 TOTAL /50

## Assessment

 LO 3 Space and Form (geometry)The learner is able to describe and represent features of and relationships between two-dimensional forms and three-dimensional objects in a variety of orientations and positions. We know this when the learner: 3.2 describes and classifies geometric figures and three-dimensional objects in terms of properties in contexts inclusive of those that can be used to promote awareness of social, cultural and environmental issues, including:3.2.1 sides, angles and diagonals and their relationships, focusing on triangles and quadrilaterals (e.g. types of triangles and quadrilaterals); 3.3 uses vocabulary to describe parallel lines that are cut by a transverse, perpendicular or intersection line, as well as triangles, with reference to angular relationships (e.g. vertically opposite, corresponding);3.4 uses a pair of compasses, a ruler and a protractor for accurately constructing geometric figures so that specific properties may be investigated and nets may be designed;3.5 designs and uses nets to make models of geometric three- dimensional objects that have been studied in the preceding grades and up till now;3.7 uses proportion to describe the effect of expansion and reduction on the properties of geometric figures;3.8 draws and interprets sketches of geometric three-dimensional objects from several perspectives, focusing on the retention of properties. LO 4 MeasuringThe learner is able to use appropriate measuring units, instruments and formulas in a variety of contexts. We know this when the learner: 4.1 solves more complicated problems involving time, inclusive of the ratio between time, distance and speed;4.2 solves problems involving the following:4.2.1 length;4.2.2 circumference and area of polygons and circles;4.2.3 volume and exterior area of rectangular prisms and cylinders; 4.3 solves problems using a variety of strategies, including:4.3.1 estimation;4.3.2 calculation to at least two decimal points;4.3.3 use and converting between appropriate S.I. units; 4.5 calculates the following with the use of appropriate formulas:4.5.1 circumference of polygons and circles;4.5.2 area of triangles, right angles and polygons by means of splitting up to triangles and right angles;4.5.3 volume of prisms with triangular and rectangular bases and cylinders; 4.7 estimates, compares, measures and draws triangles accurately to within one degree.

## Memorandum

ACTIVITY 1

• 2
• ℓ × b
• $\frac{1}{2}$ × b ×  h
• $\pi$ r 2
• ℓ × b × h
• $\pi$ r 2 h

2. Learners supply.

3. Contents

• ℓ / mℓ / kℓ / cm 3 / mm 3 etc.
• kℓ / ℓ / mℓ

#### Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Stoney Reply
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Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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biomolecules are e building blocks of every organics and inorganic materials.
Joe
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research.net
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sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
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nano basically means 10^(-9). nanometer is a unit to measure length.
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Anassong
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
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CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
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s.
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SUYASH Reply
for screen printed electrodes ?
SUYASH
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s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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Difference between extinct and extici spicies
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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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