## Thursday, February 17, 2011

### Tianna's Textbook Homework

how to find the volume of a prism

Cylinder Volume and Volume Problems

a)

V= (3.14 x r x r) x h
V=(3.14 x 5 x 5) x 23
V= 1805.5cm3

b)

V= (3.14 x r x r) x h

V = (3.14 x 14 x 14) x 12

V= 7385.28cm3

c)

V= (3.14 x r x r ) x h

V=(3.14 x 0.5 x 0.5 ) x 1.5

V= 1.1775

### Demvry's Textbook Homework

Pages 258-261
Questions 18 and 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?

a)I say this is not possible because I think there is no whole number that could be cubed to be able to equal 18.
b)She would probably need to use 27 cubes to make the largest cube possible (3x3x3).

Question:
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.

The volume of the one shaped as a cube is 343cm2.
The volume of the one shaped as a rectangular prism is 360cm2.
The volume of the one shaped as a triangular prism is 367.5cm3.

According to the volumes, the triangular prism would've the most water for Harvey the guppy to swim in.

Here are some videos!
Volume of a cube!

Volume of a rectangular prism!

Volume of a triangular prism!

http://www.math.com/tables/geometry/volumes.htm

Inform me if I made a mistake or tell me what I could improve on. Thanks.
Ps - If the letters are over or undersized, ignore it and I'll try to find a way to fix it. If I can't, I'm sorry.

### Justin Lorenzo's Math Textbook Homework

Pages 259-260 Answers to # 7, 12, 14 (Math Textbook)

7.)

A) V= B x H ÷ 2 x H

V= 12 x 7 ÷ 2 x H

V= 42cm2 x 7cm2

V= 294cm3

B) V= B x H ÷ 2 x H

V= 8.1 x 2.2 ÷ 2 x 15

V= 8.91m2 x 15m2

V= 133.65m3

C) V= B x H ÷ 2 x H

V= 320 x 210 ÷ 2 x 400 / 67 200 ÷ 2 x 4

V= 33 600mm2 x 4mm2

V= 13 440 000 mm3
12.)

Base (cm)
7
18
20

Height Of Triangle (cm)
10
10
5

Height of prism (cm)
70
1080
700

14.)

V= B x H ÷ 2 x H

V= 15 x 8 ÷ 2 x 80

V= 60cm2 x 80cm2

V= 4800 cm3

If there are any other solutions, or mistakes I have typed please feel free to comment!

Which is the correct formula for volume?
Create your own poll at Flisti.com

7.3

(picture1)

v = π r r h
v = (3.14x5cmx5xm) x 23
v = 1805.5cm3

7.4

(picture 2)

r=d/2 bxh1/2 x h2
r=25/2 40x35/2 x 140cm2
r=12.5cm2 = 98000cm3

v=π r r h
v= (3.14x12.5x12.5)x100
v=49062.5cm3

98000cm3 - 49062.5cm3 = 48937.5cm3

### HWB pg. 80 & 81 #4, 6, 8

4. Calculate the volume of each rectangular prism.
a) l = 15cm, w = 12cm, h = 3cm

v = l x w x h
15cm x 12cm = 180cm2
180cm2 x 3 = 540cm3

b)

v = l x w x h
8.5m x 7m = 59.5m2
59.5m2 x 2m = 119m3

c)

v = l x w x h
20cm x 8cm = 160cm2
160cm2 x 16cm = 2560cm3

6. Calculate the volume of each right triangular prism. Express the answer to the nearest tenth.

a)

v = b x h1/2 x h2
7.2 x 4.5cm/2 = 16.2cm2
16.2cm2 x 10cm = 162cm3

b)
v = b x h1/2 x h2
5 x 3/2 = 7.5cm2
7.5 x 8.5 = 63.8m3

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

v = b x h1/2 x h2
4 x 5/2 = 10m2
10m2 x 12 = 120m3

8. Wab needs to buy drinks for the summer barbeque. Both containers are the same price. Which one holds more?

apple juice:
v = l x w x h
6cm x 9cm = 54cm2
54cm2 x 4.5cm = 243cm3

orange juice:
v = l x w x h
6cm x 10cm = 60cm2
60cm2 x 3.75 = 225cm3

Apple juice holds more juice (y)

Here's a video:

URL of pictures:
http://www.clker.com/clipart-3934.html
http://www.ifood.tv/blog/apple-juice-health-benefits

Please tell me if I did any mistakes or what I can do better next time. (:

Cylinder Volume and Volume Problems

Chapter 7.3:

v = π r r h
v = (3.14x5cmx5xm) x 23
v = 1805.5cm3

Chapter 7.4:

Volume of cylinder: Volume of triangular prism:

r=d/2 bxh1/2 x h2
r=25/2 40x35/2 x 140cm2
r=12.5cm2 = 98000cm3

v=π r r h
v= (3.14x12.5x12.5)x100
v=49062.5cm3

98000cm3 - 49062.5cm3 = 48937.5cm3

Video:

* I meant to say cubed when I said squared on the part where i was supposed to say cubed :P

## Wednesday, February 16, 2011

### Diana's Homework Book Post.

Even numbers, Pages 78-79.

4. A)

B)

C)

6. A)

Both rectangular prisms have the volume of 200cm.

B)

Both rectangular prisms have the volume of 10.5 m3.

8.

The need to put 24.3m3 of water in the pool.

Comment if I did anything wrong.
Also , sorry that a couple of my pictures are not the right way they wouldn't want to rotate.

Chapter 7.3

Jumbo:
r= d÷2 V=(pi.r.r)x h
r= 20÷2 V=(3.14x10x10)x40
r=10cm V=314 x 40
V=12'560cm³

Popcorn Lover's:
r= d÷2 V=(pi.r.r)x h
r= 30÷2 V=(3.14x15x15)x20
r= 15cm V= 7065 x 20
V= 14'130cm³

Martha should buy the popcorn lover's one because it has a greater volume than the Jumbo one.Popcorn Lover's volume is 14,130cm³ and Jumbo's 12,560cm³.

Chapter 7.4

Outside;
r=d÷2 V=(pi.r.r)x h
r= 1÷2 V=(3.14x0.5x0.5)x10
r=0.5m V= 0.785 x 10
V= 7.85m³

Inside;
r= d÷2 V=(pi.r.r)x h
r= 0.8÷ 2 V=(3.14x0.4x0.4)x10
r= 0.4m V=0.5024 x 10
V= 5.024m³

You Subtract the volume of the inside from the volume of the outside.
7.85m³ - 5.024m³ = 2.826m³

The volume of concrete needed to make the culvert is 2.826m³

### Mike's Volume Post

Show You Know

A
) Area of Base X Height
L x W x H

8.5cm x 4cm x 5cm

170cm3

B
) L x W x H

3cm x 3cm x 3cm 3 x 3 = 9cm2

9cm2 x 3cm = 27cm3

C)
B x H
----- = H
2

9 x 5
----- = 22.cm2
2

22.5cm2 x 8cm = 180cm3

OR

5 x 9 x 8/2 = 180cm3

A website you can visit about volume.

### Casey's volume post 3, 9, 11

3. a) area of the basexheight

15 cm2 x 4 cm = 60 cm3

b) area of the basexheight

18 cm2 x 12 cm = 216 cm3

c) area of basexheight

96 cm2 x 20 cm = 1920 cm3

9. There are four ways to build a rectangular prism from 16 cm cubes.

11. area of the basexheight

10.4 cm2 x 9 cm = 93.6 cm3

p.s. sorry for no videos they would not work on my computer

a) v= (pi x r x r) x h b) v= (pi x r x r) x h

v= ( 3.14 x 5 x 5) x 23 v= (3.14 x 14 x 14) x 12

v= 78.5 cm2 x 23 cm v= 615.44 cm2 x 12 cm

v= 1805.5 cm3 v= 7385.28 cm3

c) v= (pi x r x r) x h

v= (3.14 x 0.5 x 0.5) x 1.5

v= 0.785 cm2 x 1.5 cm

v= 1.1775 cm3

Answer: 45 cm long, because they both have the same volume.

### Robin's Volume Scribe Post

2) Does the volume of a right prism depend on which face is used on the base of the calculations? Use examples to support your position.

This Question i was confused on sorry i didn't answer it .

5)Determine the volume of each right rectangular prism.

A)
L.W.H
3x4=12cm2
12x5=60cm3

L.W.H
3x5=15cm2
15x4=60cm3

B)

L.W.H 6x8=120cm2
120x8=960cm3

L.W.H
8x6=48cm2
48x20=960cm3

8)
Nina uses 15 centimeter cubes to make the base of the rectangular prism. Determine the volume if the prism has a total of 5 layers of cubes. Show your thinking

Answer) So you have 5 layer with 15cm2 then you times your centimeter like (15x5)
to get 75cm3.

10)
A water through is in a shape of a right triangular prism with base area of 1250 cm2 and a height of 100 cm. How much water can be put in there before it overflows?

it will be 125 00cm3 before it get overflows.

Here a video to understand more about volume:

Tell me if i did anything wrong.

## Monday, February 14, 2011

### Tonie's Volume Scribe Post

Volume

Base (of a prism or cylinder)
• any face of a prism that shows the named shape of the prism
• the base of a rectagular prism is any face
• the base of a triangular prism is 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 prisms of cylinder
Volume
• the ammount 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 Rectangle Prism

l x w x h
6x5=30cm^2
30cm2 x 10 = 300cm^3

Volume of a Triangular Prism
b x h/2 x h
5x7/2=17.5cm2
17.5cm2 x 10 = 175cm3

Volume of a Cylinder

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

3.14.r.r.h
3.14.4.4=50.24cm2
50.24cm2 x 10 =502.4cm3

Jumbo Container:
d/2=r
20/2=r
10=r

V=pi.r.r.h
V=(3.14 .10 .10) .40
V= 314.40
V=12,560 cm^3

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

V=pi.r.r.h
V=(3.14.15.15).40
V= 706.2 . 40
V=28,248cm^3

Martha should buy the 'Popcorn Lover's' container because the volume is bigger.

*please feel free to correct me*

## Wednesday, February 2, 2011

### Cylinder Homework

r= d/2
r=7/2
r=3.5cm

=2 .π. r. r+ 2.π.r.h
=2. 3.14 . 3.5 . 3.5+2 . 3.14 . 3.5 . 7
= 76.93 + 153.86
= 230.79cm 2

r=d/2
r=15/2
r=7.5cm

=2 .π. r. r+ 2.π.r.h
=2 . 3.14 . 7.5 . 7.5 + 2 . 3.14 . 7.5 . 18
=353.25 + 847.8
=1201.05cm 2

=2 .π. r. r+ 2.π.r.h
=2 . 3.14 . 6.5 . 6.5 + 2 . 3.14 . 6.5 . 20
=265.33 + 816.4
=1081.73cm 2

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

v=( r x r) x h
v=(3.14 x 4 x 4) x 10v=50.24m 2 x 10
v= 502.4m 3

502.4/2
=251.2m 3

Then you subtract the volume of the smaller cylinder to the bigger cylinder which will give you the amount of concrete needed for the culvert.

Concrete= 5.024m 3 - 7.85m 3
Concrete= 2.826m 3

## Tuesday, February 1, 2011

### Marie's Volume Post

Things to remember:
• The bases are circles
• Radius is half a diameter
• Diameter cuts a circle in half
• Circumference is the perimeter of a circle
• Pi is the ratio between circumference/diameter or 3.14

Formulas:
Circumference - pi (d) = c
Diameter - 2r = d or c/pi

Area of a circle:
pi (r²) or pi (r) (r)

Net of a cylinder:

Formula:
lxw = a

pi (r) (r) = a
d = 2r
r = d/2

c = pi(d)

Here are the answers on our homework.
*I'm only showing one of each (diameter, circumference, radius) because Mr. Harbeck told me to.*

Here is a link on cylinders.

A video to help you learn the surface area of a cylinder:

Cylinder Volume and Volume Problems

7.3

7.4