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

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

 

Vincent's Homework Book Post

Pages 78-79

Questions 5, 7 and 9

5. What is the volume of a right prism that has a base with an area of 15cm2 and a height of 7 cm?

7.Calculate the height of each rectangular prism.
a)

b)

9.Chad wants to cut back on the amount of treats he is eating. He has two chocolate bars to choose from. Which one has less chocolate? Show your thinking.

The one on the left has less chocolate.

Cylinder Volume and Volume Problems

(2πxrxr)+(2xrxπxh)
(2x3.14x12x12)x(2x12x3.14x15)
904.32cm2 + 1 130.4cm2

2034.72cm3

Math textbook: pg. 250-253 #2,5,8,10

No, it does not matter.
Take this rectangular prism for example (the proportions are probably strange, but you get the idea.)

v=area of base x height
v=50cm² x 4cm
v=200cm³

v=area of base x height
v=20cm² x 10cm
v=200cm³
As you can see the volume is the same.



v= area of base x height
v=12cm² x 5cm
v=60cm³

v= are of base x height
v= 15cm² x 4cm
v=60cm³



v= are of base x height
v=120cm² x 8cm
v=960cm³

v=are of base x height
v=48cm² x 20cm
v=960cm³



So, basically one centimeter cube would look like this:

And if you were to make one layer or a base out of the fifteen centimeter cubes used, it should look like this:

The area of the top of this one layer should be 15cm² so we will use that as our base.

Since the prism is made of 5 layers of those 15 centimeter cubes we will use that as our height.

v= area of base x height
v= 15cm² x 5cm
v=75cm³



Though worded differently it is basically asking for it's volume.

v= area of base x height
v= 1250cm² x 100cm
v= 125 000cm³

Here's a link to calculating volume.

And two videos explaining both rectangular prisms and cylinders:




Cylinder Volume and Volume Problems


v=π x r x r x h
v=(3.14 x 12 x 12) x 15
v= 452.16cm^2 x 15 cm
v= 6782.4 cm^3

6782.4/4= 1695.6cm^3

Assume that 1/4 of the cheese was cut.


Cylinder one:
r= d/2
r =10/2
r= 5m

v= π x r x r x h
v= (3.15 x 5 x 5) x 30
v= 78.5 m^2 x 30m
v= 2355m^3

Cylinder two:
r= d/2
r= 8/2
r=4

π x r x r
(3.14 x 4 x 4)
50.24 m^2

2335m^3/ 50.24m^2= 46.5 m

I pray that I made any sense.

Paul's Textbook post

Show you know pg. 248 and 249
Questions 1,3,7 pg. 250-253

Show you know
pg.248






V=area of base x height
V=40cm² x 22cm
V=880cm³

pg. 249










Left
V=area of base x height
V=24cm² x 7cm
V=168cm³
Right
V=area of base x height
V=56cm² x 3cm
V=168cm³
Both has the same volume

Question 1











In their calculation Charlotte made a mistake measuring the right rectangular prism because she did not use the prism's height. Instead she should have done this.
V=area of base x height
V=63cm² x 3cm
V=189cm³

Question 3


A)
V=area of base x height
V=15cm² x 4cm
V=60cm³
B)
V=area of base x height
V=18cm² x 4cm
V=216cm³
C)
V=area of base x height
V=96cm² x 20cm
V=1920cm³

Question 7







a)
h=volume divided by area of base
h=32cm³ divided by 8cm²
h=4cm
b)
h=volume divided by area of base
h=35cm³ divided by 5cm²
h=7cm
c)
h=volume divided by area of base
h=36cm³ divided by 9cm²
h=4cm

Here's a link on how to find the volume of a cylinder and a right rectangular prism.

Cylinder


Right rectangular prism


Cylinder Volume and Volume Problems
7.3


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

v=(π.r.r).h
v=(3.14x10x10)x40
v=314x40
v=12 560cm³

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

v=(π.r.r).h
v=(3.14x15x15)x20
v=706.5x20
v=14 130cm³
Martha should choose popcorn lover's conatiner because it has more volume than the jumbo container.

7.4

a)r=d/2
r=120/2
r=60cm

v=(π.r.r).h
v=(3.14x60x60)x18
v=11 304x18
v=203 472cm³

b)v=lxwxh
v=30x22x20
v=13 200cm³

c)volume of wading pool / volume of pail
203 472 / 13 200= 15.4 pails of water

Volume of cylinder