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!