## Thursday, February 17, 2011

### 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?

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!