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

Glenesse's Homework Book Post

Homework Book

Pages 78-79

Even #'s 4, 6, 8

Questions:

4. Calculate the volume of each prism or cylinder.

a)

b)

c)

Answers:

4)-a) Area of base X height

100 cm² X 4 cm = 400 cm³

b) Area of base X height

113 cm² X 3 cm = 339 cm³

c) Area of base X height

80 cm² X 12 cm = 960 cm³

Question:

6) Which rectangular prism has the larger volume? Show your thinking.

a)

b)

Answers:

6)-a)

1-Area of base X height

40 cm² X 5 cm = 200 cm³

2-Area of base X height

20 cm² X 10 cm = 200 cm³

They both have a volume of 200 cm³.

b)

1-Area of base X height

10.5 m² X 1 m = 10.5 m³

2-Area of base X height

3 m² X 3.5 m = 10.5 m³

They both have a volume of 10.5 m³.

Question:

Nikki and Taylor have to fill the pool this summer. The area of the pool bottom is 27 m². The height that the water needs to be is 0.9 m. How much water do they need to put in the pool?

Answer:

Area of base X height

27 m² X 0.9 m = 24.3 m³

Click Here to learn more about volumes.

Here is a video on how to find the volume of a prism.

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 x 10) x 40
v=314cm^2 x 40cm
v=12560cm^3

Popcorn Lovers
r=d/2
r=30/2
r=15cm

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

Martha should buy the Popcorn Lovers container

a)

r=d/2

r=120/2

r=60cm

v=π x r x r x h

v=(3.14 x 60 x 60) x 18

v=11304cm^2 x 18cm

v=203472cm^3

b)

v=l x w x h

v=30 x 22 x 20

v=660cm^2 x 20

v=13200cm^3

c) 203472cm^3/13200cm^3 = 15.4 pails

Patrick's Math Notes Post

VOLUME





BASE (of a prism of cylinder)
-Any face of a prism that shows the named shape of the prism.
-The base of a rectangular prism is any face.
-The base of a triangular prism a triangular face.
-The base of a cylinder is a circular face.

HEIGHT (of a prism or cylinder)
-The perpendicular distance between the two bases of a prism or cylinder.

VOLUME
-The amount of space an object occupies
-Measured in cubic units

ORIENTATION
-The different position of an object formed by translating, rotating or reflecting the object.

____________________________________________________________________


Volume of a Rectangular Prism.


area of base X height
l x w
6 x 5 = 30cm²

30cm² x 10 cm = 300 cm³

Volume of a Triangular Prism.



area of base X height

b x h /2
7 x 5 / 2 = 17.5 cm²

17.5cm² x 10 cm = 175cm³

Volume of a Cylinder



area of base X height
π X r X r
3.14 X 5 X 5 = 78.5 cm²

78.5cm² X 10 cm = 785 cm³
___________________________________________________________________

These three videos should help you how to find the volume of a shape.





____________________________________________________________

Cylinder Volume and Volume Problems



r = d/2
r = 0.26 m/2
r = 0.13 m^2

V = (π x r x r) x h
V = (3.14 x 0.13^2) x 2.4m
V = (0.05m^2) x 2.4 m
V = 0.12m^3

0.12m^3 x 35 = 4.2, (round up) = 5m^3

The volume of concrete required is 5m^3.


a)Volume with the missing piece = l x w x h
Volume with the missing piece = 10cm x 16cm x 10cm
Volume with the missing piece = 1600cm^3

Volume of missing piece = l x w x h
Volume of missing piece = 10cm x 6cm x 5cm
Volume of missing piece = 300cm^3

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

The volume is 1300cm^3

b) You can check your answer by dividing the shape into separate rectangular prisms.