John's Cylinder Homework

a)r-5 h-20
V=π x r x r x h
V=3.14 x 5 x 5 x 20
V=1570 cm3

b)r-.5 h-1
V= π x r x r x h
V=3.14 x .5 x .5 x 1
V=0.785 m3

c)r-9 h-7.5
V= π x r x r x h
V=3.14 x 9 x 9 x 7.5
V=1907.55 cm3 

 
r-.25 h-20
V=π x r x r x h
V=3.14 x .25 x .25 x 20
V=3.925 cm3 

Leea's Volume And Volume Problems

Chapter 7.3



r =d/2
r = 8/2
r= 4 m

V= πxrxrxh
V= 3.14 x 4 x 4 x 10
V= 50.24 m^2 x 10 m
V= 502.4 m^3

V= 502.4 m^3/2
V= 251.2 m^3




r= d/2
r=10/2
r= 5

V= π x r x r x h
V= 3.14 x 5 x 5 x 30
V= 78.5 cm^2 x 30 cm
V= 2355 cm^3

r= d/2
r= 8/2
r= 4

h = V/ π x r x r
h = 2355 cm^3/ 3.14 x 4 x 4
h = 2355 cm^3/ 50.24 cm^2
h= 46.875 cm or 46.9 cm

Chapter 7.4


V= π x r x r x h

V= 3.14 x 0.5 x 0.5 x 10

V= 0.785 m^2 x 10 m

V= 7.85 m^3

V= π x r x r h

V= 3.14 x 0.4 x 0.4 x 10

V= 0.5024 m ^2 x 10 m

V= 5.024 m^3

V= 7.85 m^3 - 5.024 m^3 v= 2.826 m^3


LINKS:
http://www.youtube.com/watch?v=QhHYOZ0Rf4I
http://www.youtube.com/watch?v=bON3X7UpFRE

Chelsea's Cylinder Volume and Volume Problems

7.3, Page 266

a)

V=πxrxrxh
V=(3.14x4x4)x12
=50.24cmx12
=602.88

b)

V=πxrxrxh
V=(3.14x1x1)x7
= 3.14cm2x7
= 21.98

c)

V= πxrxrxh
V= (3.14x6x6)x37.5
= 113.04cm2x37.5
= 4329

d)

V=πxrxrxh
V= (3.14x2.25x2.25)x19.5
= 15.90cm2x19.5
= 310.05


----------------------------------------
7.4, Page 273


































The answer is 1130.4cm

Arun's Volume scribe

4. a) V = b x h x l

V = 1 x3 x 5

1 x 3 = 3 cm2

3 cm2 x 5 cm2 = 15 cm2

V = 15 cm3

b)V = b x h l

V = 11 x 6 x 12

11 x 6 = 66 cm2

66 cm2 x 12 cm2 = 792 cm2

V = 792 cm2

c) V = b x h x l

V = 4 x 2 x 6.2

4 x 2 = 8 cm2

8 cm2 x 6.2 cm2 = 49.6

V = 49.6 cm2

5. Questions: Answer:

a) l = 2 m, w = 2 m, h = 10 m a) l x w = b V = b x h

b) l = 8 cm, w = 7 cm, h = 9 cm V = 80 cm3

c) l = 11.7 mm, w = 6.3 mm, b)l x w = b V = b x h

h = 2.9 mm V = 4, 032 cm 3

d) l = 6.2 cm, w = 6.4 cm, h = 6.4 c c)l x w = b V = b x h

V = 213 , 759 cm3

d) l x w = b V = b x h

V = 253, 952 cm3

6. a) V = s x s x s

10 x 10 x 10

V = 1000 cm3

b) V = s x s x s

3 x 3 x 3 V

V= 28 cm3

c) V = s x s x s

2.5 x 2.5 x 2.5

V = 15. 625 cm3


Cylinder Volume and Volume Problems

a) V = d/2 =r
10/2 = 5

V=

Sandra's Volume Post

11. Copy and complete the chart:
blue=answer

Length Width Height Volume

a)7cm 2cm 5cm 70cm3

l

b)12cm 9cm 10cm 1080cm3

c)16cm 15cm 5cm 1200cm3

You can easily fill in this chart by simply asking yourself what multiplied by what equals the volume or creating an algebraic equation for each one. For example: a) 7x2=14, so 14xa=70m3, you replace the variable (a) with the number that best suits that equation which is 5. So thats how I figured out question 11.

16. Cindy’s aquarium stands 75 cm tall and
has a base that measures 1.2 m × 80 cm.
At one point during the initial fi lling, the
aquarium has a 12-cm depth of water in
it. Cindy needs to fi ll it to 15 cm from the
top before she adds the fi sh. Draw a
diagram and label the dimensions of the
aquarium. Determine how much more
water Cindy must add before she puts in
the fi sh.

Red=Math information

Scince you need a 15cm gap from the top you need to subtract 12 from 75 which is 63 and then you subtract 15 from 63 and you get 48. Now we have to find the volume of water we need to use in the tank.

V=lxwxh

v=120cmx80cmxh

v=9600cm2x48cm

v=460 800 cm3.

So Cindy needs to add 460 800cm3 of water before she adds the fish.

17.
A contractor is excavating a rectangular
hole 10 m × 12 m × 3 m to pour the
foundation for a house. A dump truck
with a capacity of 9 m3 is used to haul
away the excavated soil. How many trips
does the truck need to make?

Find volume of rectangular hole:

V=lxwxh

v=10mx12mxh

v=120m2x3m

v=360m3

360m3/9m3=40m3

So the truck driver will have to make 40 trips.

Cylinder Volume and Volume Problems

Cylinder Problem

Jumbo

d=r/2

d=20cm/2

d=10cm

v=πr^2 h





v=(3.14 10cm^2) 40cm





v=314cm^2 40cm





v=12560cm^3









Popcorn Lovers









r=d/2




r=30cm/2




r=15cm
v=πr^2 h




v=(3.14 15cm ^2) 20cm




v=706.5cm^2 20cm




v=14130cm^2









If Martha wants more popcorn for her money, she should get the popcorn lovers because it has a greater volume, that being said, you can fit more popcorn into it.







Volume Problem
A concrete culvert that is 10 cm long has an inside diameter of 0.8m and an outside diameter of 1m. Determine the volume of concrete required to make the culvert to the nearest tenth of a cubic centimetre.










Outside Diameter
r=d/2
r=1/2
r=0.5m
v=πr^2 h
v=(3.14 0.5^2) 10m

v=0.785cm^2 10m

v=7.85m^3



Inside Diameter

r= d/2
r=0.8/2
r=0.4m

V=πr^2 h


V=(3.14 0.4^2)h


V=0.5024m^3



To find the volume subtract the inside diameter from the outside diameter.



7.85m^3-o.5024m^3=7.3476m^3

Now we have to convert meters into centimetres.

We can do that by multiplying 7.3476 by 100, and that equals 734.76cm^3.



So you need 734.76cm^3 of concrete to make the culvert.

Duyen's Textbook Page 261 Questions 18 & 19

Question 18

Suki has 30 small linking cubes.

a) She wants to use 18 of them to make a large cube. Is this possible? Why or why not?

b) What number of linking cubes would she use to construct the largest cube she can possibly make?

Answers:

a) Suki can not make a large cube using 18 small linking cubes because 18 is not a cubed number.

Work:

1 x 1 x 1= 1³ Under 18 cubes

2 x 2 x 2= 8³ Under 18 cubes

3 x 3 x 3= 27³ Over 18 cubes

b) Suki needs 27 linkings cubes in order to make a 3 by 3 cubes in order to make the largest cube with a maximum amount of 30 small linking cubes.

Work:

1 x 1 x 1= 1³

2 x 2 x 2= 8³

3 x 3 x 3= 27³ Maximum amount for constructing a cube using under 30 linking cubes

4 x 4 x 4= 32³ Over 30 small linking cubes


19. Melissa has three glass vases. She wants to use one as a decorative fish tank for Harvey the guppy. Which will give Harvey the most water to swim in?

Volume of Cube:

Side x Side x Side= Area of cube

7 cm x 7 cm x 7 cm = 343 cm³

Volume of Cube= 343 cm³

Volume of Rectangular Prism:

Area of Base x Height= Area of Rectangular Prism

Length x Width= Area of Base

10 cm x 9 cm= 90 cm²

Height= 4 cm

90 cm x 4 cm= 360 cm³

Volume of Rectangular= 360 cm³


Volume of Triangular Prism:

(Base x Height) / 2 x Height= Volume of Triangular Prism

(7 cm x 5 cm) / 2 x 21 cm=

35 cm / 2 x 21 cm=

17.5 cm x 21 cm= 367.5 cm³

Volume of Triangular Prism= 367.5 cm³

Harvey will have the most water to swim is in the triangular prism.

Here is a link to educate you if you are still unsure about cubing or volume. Also here is a volume calculator to help you with volume work.

Video About The Volume Of A Rectangular Prism

Video About The Volume Of A Cube

Video About The Volume Of ATriangular Prism

Problem From Chapter 7.3

1695.6 cm³ was cut from the block of cheese. My assumption that I made is that approximately one-quarter of the block of cheese was cut off.

Work:
Formula: (π x r x r) x h= v

(3.14 x 12cm x 12cm) x 15cm= v

452.16cm² x 15cm=6782.4cm³

6782.4cm³ / 4= 1695.6cm³

Volume= 1695.6cm³

Problem From Chapter 7.4

The capacity of the pipe, to the nearest tenth of a cubic centimetre is 1130.4cm³.

Work:

Outer Volume:

d/2= r

10cm/2= 5cm

( π x r x r) x h= v

(3.14 x 5cm x 5cm) x 40cm= v

78.5cm² x 40cm= 3140cm³

Volume of Outer Pipe= 3140cm³

Inner Volume:

d/2= r

8cm/2= 4cm

(π x r x r) x h= v

(3.14 x 4cm x 4cm) x 40cm= v

50.24cm² x 40cm= 2009.6cm³

Volume of Inner Pipe= 2009.6cm³

Subtraction of Both Pipes:

Formula outer pipe - inner pipe= capacity of pipe

3140cm³ - 2009.6cm³= 1130.4cm³

Capacity of Pipe= 1130.4cm³

EXTRA

Here is a link of a volume of a cylinder calculator.

Video About Finding The Volume Of A Cylinder

My Cylinder Video

I am extremely sorry if my voice sounded weird and that it sounded disorganized because I got a cold and I didn't have a script or practice. In other words to be honest I just made up the whole thing in my head while recording this video. Also if there are any problems feel free to comment or suggest below in the comment box. I will try to accommodate you to the best of my ability. In addition I might have made some spelling errors during, but I have fixed them after discovering them. Good luck on our upcoming test on March 2,2011!

Homework Book Pages 4, 6, and 8

a= l x w

a= 15 x 12

a= 180cm²

v= area of base x height

v= 180cm² x 3cm

v= 540cm³

a= l x w

a= 8.5 x 7

a= 59.5cm²

v= area of base x height

v= 59.5m² x 2m

v= 119m³

a= l x w

a= 20 x 8

a= 160cm²

v= area of base x height

v= 160cm² x 16cm

v= 2560cm³

v= b x h/2 x h²

7.2 x 4.5/2 = 32.4cm²

v= 32.4cm² x 10cm

v= 324cm³

v= b x h/2 x h²

3 x 5/2 = 7.5m²

v= 7.5m² x 8.5m

v= 63.75m³

c) A prism where the base of the triangle is 4m, the height of the triangle is 5m, and the prism height is 12m.

v= b x h/2 x h²

4 x 5/2 = 10m²

v= 10m² x 12m

v= 120m³

Pear juice:

a= l x w

a= 9 x 6

a= 54cm²

v= area of base x height

v= 54cm² x 4.5cm

v= 243cm³

Pineapple juice:

a= l x w

a= 10 x 6

a= 60cm²

v= area of base x height

v= 60cm² x 3.75cm

v= 225cm³

The second juice box holds more.

Here's a link that tells you more about volume.

This tells you how to find the volume of a rectangular prism.

Cylinder Volume and Volume Problems

d/2= r
8/2= r
4m= r

V= π x r x r x h
V= (3.14 x 4 x 4) x 10
V= 50.24m^2 x 10m
V= 502.4m^3

502.4m^3/2 = 251.2m^3The volume of the semicircular trough is 251.2m^3.

Outside:
d/2= r
1/2= r
0.5m= r

V= π x r x r x h
V= (3.14 x 0.5 x 0.5) x 10
V= 0.785m^2 x 10m
V= 7.85m^3

Inside:
d/2= r
0.8/2= r
0.4m= r

V= π x r x r x h
V= (3.14 x 0.4 x 0.4) x 10
V= 0.5024m^2 x 10m
V= 5.024m^3

7.85m^3 - 5.024m^3 = 2.8m^3

Kevin's show you know post

Math Information : 4 children

volume of the rectangular prism = area of base x height
To find the area of the base = l x w
area of the base = 40cm x 24cm = 960cm²
Volume = Base x Height
Volume = 960cm² x 20cm
Volume = 19 200cm³
The total volume of the mini building blocks are 19 200cm³.

To find volume for 4 children you divide by 4.
19200 ÷ 4 = 4800cm³

Each of Mr.Chin's children will receive a volume of 4800cm³ building blocks.

Thanks for taking the time to look at my post, if you have any free time you should play this fun volume game and watch the videos below.
P.S. If you lost your notes or forgot the formula please checkout Patrick's note post. ←Click

This video will be talking about the volume of cones.


This video will be talking about the volume of prisms.


This video will be talking about the volume of pyramids.


Cylinder Volume and Volume Problems

The maximum volume of the capture envelope is 3234.9065cm³
d÷2 = r ╥r² x h = v
20.3÷2 = 10.15cm (3.14 x 10.15 x 10.15) x 10 = v
323.49065cm² x 10 = v
3234.9065cm³ = v

Laura, an office manager, has purchased a carton that is 300 cm × 400 cm × 600 cm to store 9000 boxes of files. Each box has dimensions 30 cm × 26 cm × 10 cm. Calculate whether all of the files will fit in the carton.
Yes it is enough, 1 carton can hold all files.
The volume of the carton is 72 000 000cm³.
(l x w) x h
(300 x 400) x 600
120 000cm² x 600cm
72 000 000cm³

(l x w) x h
(30 x 26) x 10
780cm² x 10cm
7800cm³
The volume of 1 box is 7800cm³, we need 9000 so multiply by the amount.
7800cm³ x 9000 = 70 200 000cm³

Homework Book- Pg.80-81 #5, 7, 9

5. Calculate the volume of each cube.
-Express your volume to the nearest tenth.





7. Calculate the volume of the contents of each container.




9. A contractor if buying cement for 100 triangular parking barriers. How much concrete does she need?



She needs 7.2m of concrete.





Cylinder Volume and Volume Problems



Jumbo
r=d/2
r=20/2
r=10cm

v=π x r x r x h
v=(3.14 x 10 x10) x 40
v=314cm^2 x 40cm
v=12560cm^3

Popcorn Lover's
r=d/2
r=30/2
r-15cm

v=π x r x r h
v=(3.14 x 15 x 15) x 20
v=706.5cm^2 x 20
v=14130cm^3

Martha should buy the Popcorn Lover's container.


a)
v=l x w x h
v=10 x 10 x16
v=1600cm^3

v=l x w x h
v=5 x 6 x 10
v=300cm^3

v=1600cm^3 - 300cm^3
v= 1300cm^3

b) You can check your calculations by dividing the shape into a different set of rectangular prisms.

Jae Anne's Volume Scribepost

Textbook pg 250 - 252
# 3, 9, 11, and 15

3. Determine the volume of each right prism or cylinder.

a)

V = area of the base x height

    = 15 cm² x 4 cm

    = 60 cm³

b)

V = area of hte base x height

    = 18 cm² x 12 cm

    = 216 cm³

c)

 

V = area of  the base x height

    = 96 cm² x 20 cm

    = 1920 cm³ 

9. How many ways can you build a rectangular prism from 16 centimetre cubes? Use diagrams or centimetre cubes to show your designs.

11.  José is having vegetable soup. The area of the base of the soup can is 10.4 cm², and the height is 10 cm. When José opens the can, he sees that the soup comes up to a height of only 9 cm. What volume of soup is in the can?  

 

 V = area of the base x height

     = 10.4 cm² x 9 cm

     = 93.6 cm³ 

15.  The International Space Station is shaped like a cylinder that has a cross-sectional area of 615 m² and a length of 44.5 m. The living space for the astronauts is 425 m³. What percent of the volume of the space station is used for living?

V = area of the base x height

    = 615 m² x 44.5 m
    = 27367.5 cm³

I can't find the percent  of the space station used for living.. I tried what we did on percents but I can't.. I'm sorry.. :(

Here's the correct answer nmber 15.

425/27367 = 0.155 or 0.16

0.16 x 100 = 1.6%

Here is a  link to know more about volume.

Cylinder Volume and Volume Problems

Chapter 7.3

V = πr²h
    = (3.14 x 4²) x 10             r = d/2
    = 50.24 m² x 10 m             = 8/2
    = 502.4 m³                          = 4 m

    = 502.4 m³/2
    = 251.2 m³



Chapter 7.4

V = πr²h

    = (3.14 x 0.5²) x 10

    = 0.785 m² x 10 m

    = 7.85 m³

V = πr²h

    = (3.14 x 0.4²) x 10

    = 0.5024 m² x 10 m

    = 5.024 m³

    = 7.85 m³ - 5.024 m³

    = 2.826 m³