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FOURTH GRADE / SOLID GEOMETRY 3.1 / SIMPLE BASIC SOLIDS

MATHEMATICS IS EASY. PROVIDED THAT ONE WORKS ENOUGH .
ENOUGH IS SKILL DEPENDENT, HAVE TO FIND "ENOUGH" FOR YOUR SIZE.

   SOLID SHAPES WE WILL INVESTIGATE ARE
 ♦ 
CUBES, PRISMS, PYRAMIDS, CONES and SPHERES
 ♦ THIS TIME WE WILL INVESTIGATE the CUBE AS THE BASIC SHAPE.

THERE IS ONLY ONE GOLDEN RULE:
1. EACH SHAPE HAS TO BE STUDIED SEPARATELY.
y
1. What is a dice basically ?

!
In case of need for tips get the cursor on "y" or for help click at "ry1/2" .
RY1 RY2



a) a rectangular solid
b) a solid
c) a cube
d) a sphere


A cube is the 3 dimensional form of a square, each side is of equal length and each face angle at the corners is 90° i.e. adjacent faces perpendicular.
y
2. A cube is cut by a plane equidistantly from one of the corners. What will be the intersection of the plane with the cube ?

!
In case of need for tips get the cursor on "y" or for help click at "ry1/2" .

RY1 RY2



a) isosceles triangle
b) right triangle
c) equilateral triangle
d) obtuse triangle
The type of triangle is pretty clear but have please a look at ry1 .
Corner is used here in the sense of "the place at which two converging lines meet". Vertex should be the term.
3. How many unit squares is the surface area of a cube of unit sides ?

a) 6
b) 4
c) 8
d) 3
The area of a surface is 1 unit square . There are 6 of them.
4. A net is a two-dimensional figure that can be folded into a three-dimensional object. Which of the nets below will form a cube ?

!
a) only I
b) both
c) none
d) only II
Both have 6 faces but ... .
5. How many nets may there be for a cube ?

Ref.-1        Ref.-2


a) 7
b) 17
c) 11
d) 21
Try first and if you happen to find a number below 10 or above 12, look at the references given .
6. How many surface and volume diagonals does a cube totally have ?

a) 12
b) 14
c) 10
d) 16
Each surface hes 2 diagonals and there are ... volume diagonals .
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7. A cube has 6 faces, 4 lateral faces, 2 bases, 8 vertices, 4 lateral edges and ... base edges .
( Ref.- Figures )
( Ref.- Bases )

!
a) 8
b) 4
c) 6
d) 12
It has 2 bases .
Regarding the controversy on the number of bases look please at Ref.-Bases . In short :It has 6 potential bases as it floats. It is not easy to speak about floating objects, so we put it on a base in an orientation (say coordinate system or a room). Bottom and top are given equal rights to be bases. It could only be the bottom. Do not give much weight to this, there is controversy but it is not important.
8. All sides are equal and of unit length. Why is the figure shown below of unit volume ?

!


a) it has unit sides
b) it is a cube
c) by definition
d) it is rectangular
Definition (of volume of a cube): The number of cubic units that will exactly fill a cube.
To look for unit spheres would certainly be tedious .
9. All sides of small cubes are of unit length. How big is is the volume of the shape given in the figure below ?

!


a) 6 unit3
b) 16 unit3
c) 10 unit3
d) 8 unit3


1 side is 4 units of length .
10. In the figure below there is a cube and cylinder of equal volumes (1000 cm3 i.e. 1 Liter). Which one is supposed to be more accurate as a unit of measuring liquid volume ?

!


a) none
b) both
c) the cylinder
d) the cube
We call them a liter but no unit of measurement can be exact and infinitely accurate, it must have a finite accuracy .
11. Our units of measuring liquid volumes are mostly cylindrical. Why ?

a) it is more accurate
b) ease of production and use
c) its shape is perfect
d) its shape is beatiful
They are mostly out of glass or sheet of metal .
12. The figure says the volume of a rectangular solid is height x width x breadth on the one side and writes V = l3 on the other. Can you explain the reason ?

!


a) error
b) cubic shape
c) faces are compact
d) shape is compact
Easy to guess .
13. In the figure below seen are 3 rubix cubes all same by construction. What should be the color of the face opposite to the red ?

!
a) yellow
b) green
c) orange
d) claim is false
Check the claim first !
Claim can not be true; on the third cube there are faces having orange and red adjacent.
14. In the figure below there are 3 rubix cubes having the same colors on the faces . What should be the color of the face oppopsite to red ?

!
a) orange
b) yellow
c) green
d) white
All colors are to be seen at the third cube of the previous question. The 6th color must be orange.
15. Below is a Rubik's Cube. Each of the six faces is covered by nine stickers, among six solid colours (traditionally white, red, blue, orange, green, and yellow).
How many stickers are not to be seen ?

!


a) 36
b) 27
c) 24
d) 18
Just count. Three faces can not be seen and on them there are ... stickers.
16. How many faces of cubelets (small cubes) are not stickered by a Rubik's cube ?

!


a) 112
b) 108
c) 98
d) 88
27 cubelets have ... faces; ... of them are stickered .
17. How many cubelets are there by A Rubik's Cube that are completely not stickered ?

!


a) 8
b) 4
c) 2
d) only 1
The answer is trivial but let us be sure. let us count the stickered ones.
Begin by red in front. There are 9 stickered. Turn clockwise and say green. You find 9 but 3 of them already considered so 6. An additional 6 from orange and we have a total of 21 up to now. Blue adds only 3 and we obtain a total of 24.
18. How many small cubes are there by a Rubik's Cube that has only 2 stickers ?

!


a) 8
b) 12
c) 16
d) 10
The ones at the vertices have 3; a total of 8.
The ones in the middles of the faces each have only 1 ; a total of 6. One has none.
19. How is the shape in the figure below called ?

!


a) prism
b) rectangled
c) rectangular solid (prism)
d) cubic prism
Sometimes "... prism" may still be used .
20. Which choice gives the volume of a rectangular solid ?

!


a) V = π x (w x d x h)
b) V = 1/2 x (w x d x h)
c) V = 2 x w x d x h
d) V = w x d x h
w stands for width, d for depth and h for height .
21. Which choice gives the surface area of a rectangular solid ?

!


a) 2 x (wxh + wxd + hxd)
b) (wxh + wxd + hxd)
c) 4 x (wxh + wxd + hxd)
d) π x (wxh + wxd + hxd)
Each surface has its congruent .
y
22. A rectangular solid is cut from another bigger one and the shape seen in the figure below is obtained. What is the volume of the resulting shape based on the data given in the figure ?

In case of need for tips get the cursor on "y" or for help click at "ry1/2".

RY1 RY2



a) 176 cm.3
b) 187.5 cm.3
c) 137.5 cm.3
d) 125 cm.3


Well, this is a relatively easy problem that can be solved by trial and error. The generalized form is "two equations with two unknowns" and this may be considered to be a good introduction. In our tests we usually ask questions of this kind. We want you to learn them as early as possible. For the gifted among you these will pose no problem at the fourth grade.
Average students are supposed to skip them. Have a look at the ry1 for details .
23. What is the surface area of the rectangular solid cut out from the bigger shape (rectangular solid again)?



a) 37.5 cm2
b) 50 cm2
c) 75 cm2
d) 100 cm2
Do not forget top and bottom .
24. What is the volume of the rectangular solid cut out from the bigger shape (rectangular solid again) ?



a) 62.5 cm3
b) 67.5 cm3
c) 32.5 cm3
d) 37.5 cm3
Bottom area is 12.5 cm.2
25. What does the sum of the answers of question 22 and question 24 give ?

a) The volume of the cut rectangular shape ; 125 cm.3
b) The volume of the uncut rectangular shape ; 125 cm.3
c) The volume of the cut rectangular shape ; 250 cm.3
d) The volume of the uncut rectangular shape ; 250 cm.3
The trend is conserved.
This is the feedback!

THANK YOU FOR YOUR VISIT; HOPE WE COULD BE OF USE.
FOR MUTUAL BENEFIT YOU MAY USE OUR FORUM.
© 2011 , İsmail GERMAN. ALL RIGHTS RESERVED
PLEASE PREFER GIVING LINK IF THAT SUFFICES

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