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4.7 Volume

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Mathematics

Perimeter, area and volume

Educator section

Memorandum

23.4

a) 108 cubic cm

b) 72 cubic cm

c) 23,625 cubic cm

d) 108 cubic cm

23.5

a) 20 cubic cm

b) 63 000 cubic mm

c) 24 000 cubic cm

d) 1 728 cubic cm

e) own answer

Leaner section

Content

Activity: volume [lo 4.2, lo 4.3]

23. VOLUME

23.1 Did you know?

The amount of space that is taken up by a solid body is called the volume of the body.

The internal volume is thus the space inside a hollow container. It is also called the capacity or contents of the container.

23.2 IMPORTANT to REMEMBER!

Volume is measured in cubic measuring units

We use the following units:

cubic mm : mm³

cubic cm : cm³

cubic m : m³

1 cm³ (cubic centimetre) is a cube with a length, breadth and height of 1 cm.

1 cm³ = 1 cm x 1 cm x 1 cm

= 10 mm x 10 mm x 10 mm

= 1 000 mm3

1 m³ = 1 m x 1 m x 1 m

= 100 cm x 100 cm x 100 cm

= 1 000 000 cm³

23.3 Also LEARN the following:

Volume of a rectangular prism is length x breadth x height

Volume of a cube is y³ y = (length, breadth and height)

23.4 Use the formula: volume = length x breadth x height

to calculate the volume of the following figures:

a)

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b)

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c)

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d)

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23.5 a) Calculate the volume of the following in cm3:

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b) Calculate the volume of the following in mm3

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c) What is the volume of the figure in cm3?

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d) Calculate the volume of a cube with a length of 12 cm.

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e) Estimate the volume of the box of chalk in your classroom

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23.6 CLASS DISCUSSION

How will you determine the volume of an irregular figure, e.g. a stone?

23.6.1 Did you know?

A Greek Mathematician, Archimedes, discovered how to calculate the volume of an irregular figure while he was bathing! He saw how water flowed over the edge of the bath when he climbed in. He realised that if he could measure the volume of water that his body displaced, then he could measure the volume of his own body. Archimedes was so excited by this realisation that he jumped out of the bath and ran down the street stark naked shouting, “EUREKA!” (I have found it!)

23.6.2 Follow the following steps and see if you can measure the volume of a stone that you have picked up outside.

a) Fill a cup completely to the top with water and put the cup in a bigger container. Remember to see precisely how many mℓ water you have in the cup!

b) Slowly lower the stone into the cup. Make certain that the water that overflows lands in the bigger container.

c) Measure the amount of water in the container by pouring it into a measuring cup.

d) Your stone has a volume of 1 cm3 for each mℓ of water that overflowed because 1 mℓ = 1 cm³.

e) What is the volume of your stone? .__________________________________

Assessment

Learning Outcome 4: The learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.

Assessment Standard 4.2: We know this when the learner solves problems;

Assessment Standard 4.3: We know this when the learner solves problems using a range of strategies.

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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