Finding The Solution

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Finding The Solution

• Drill 10.8
• Problem Number 4
• Drill 10.10
• Problem Number 4

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Drill 10.8 4

• A sealed rectangular container 6cm by 12cm by
  15cm is sitting on its smallest face. It is
  filled with water level 6cm from the top. How
  many centimeters from the bottom will the water
  level reach if the container is placed on its
  largest face?

3
Figuring OutPart One
Volume Length Width Height
OR Volume Base Height
Height 15 cm Length 12 cm Width 6 cm
Base Length Height
Water Height 15cm - 6cm Water Height 9cm
Steps a) Draw the figure as the question is
requesting. That is to draw the rectangular
container on its smallest side. b) The problem
tells you that the rectangular container is 6cm
by 12cm by 15cm but if it is sitting on the
smallest face then the height will be 15cm,
length 12cm, and width 6cm. As shown on the
picture at the left hand corner. c) The problem
also addresses that the water is filled into the
container 6cm away from the top. In order to
find the height of the water, do this Start
height - 6cm water height Minus 6cm is
because 6cm away from the top.
15cm - 6cm 9cm Water height is 9cm. d)
Now you have all the numbers to solve the
problem. e) To find the area of the base you
times 12cm and 6cm. Then you will get 72cm2 and
that is the area of the base. f) Next is to find
the volume. You do that by multiplying 72cm and
9cm. The reason why 9cm not 15cm, is because
they want the volume of the water not the
container. The volume will be 648cm3. g) This is
the first part of the question.
15 cm
9 cm
6 cm
12cm
Base 12 cm 6 cm Base 72 cm2
Volume 72 cm 9 cm Volume 648 cm3
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Figuring OutPart Two
Steps a) This is the second part of the question.
You have to draw the container on its largest
face. An example of this is at the left. b)
The length 15cm, width 12cm, and height 6cm. c)
The volume stays the same because it is the same
container and water. d) The question is asking
for the height of the water when the container is
laid on the largest face. So in order to find
the height, you first have to find the are of the
base. That is 15cm times 12cm and that equals
180cm2. e) After finding the base area. You have
to find the height and you do that like
this Volume 648cm3 648 180 (h) h
3.6cm f) The answer to the problem is finally
height 3.6cm
Base 15cm 12cm Base 180cm2
6cm
Volume 648cm3 Volume 180 (h) 648 180 (h) h
3.6cm
3.6 cm
12cm
15cm
The volume stays the same no matter which side
you lay the container on.
5
Drill 10.10 4

• A cube with edges 6in long just fits in a sphere.
  The diagonal of the cube is the diameter of the
  sphere. Find the volume of the space between the
  sphere and the cube.

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Big ProblemPart One
Pythagorean Theorem a2 b2 c2
R Radius D Diameter R D/2
62 62 C2 36 36 C2 72 C2 C 8.5 in
8.52 62 D2 72.25 36 D2 108.25 D2 D
10.39 in
R 10.39/2 R 5.196 in
Sphere Volume 4/3 (3.14) (radius)3 Volume 4/3
(3.14) (5.196)3 Volume 187.04 (3.14) Volume
587.62 in3
Equation for finding empty space Volume
Sphere - Cube Volume 587.62 - 216
Volume 371.7 in3
Diameter
Cube Volume Length Width Height Volume 6
6 6 Volume 216 in3
6 in
10.39 in
8.5 in
Length 6 in Width 6 in Height 6 in
6 in
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Big ProblemPart Two
Steps a) You start of drawing the diagram. An
example is shown on the pervious slide at the
bottom right corner. The cubes sides are all six
inches. b) After drawing you draw the diameter of
the sphere. Next you draw a diagonal line on the
bottom base of the cube. These lines will form
two right triangles. c) Start with the base right
triangle. Use the Pythagorean Theorem to find
the third side or hypotenuse leg.
Equation 62 62 C2 The answer is on
the pervious page. d) Then you will use the
Pythagorean Theorem again when solving for the
diameter. Equation 8.52 62 D2 8.5
came from the first Pythagorean Theorem. e) After
that you will find the radius by using this
equation R D/2 f) Then you could use the
radius to find the volume of the sphere like
this Volume 4/3 (3.14) (radius)3 Plug in
the radius to find the answer. g) After finding
the volume of the sphere, next comes the volume
of the cube. The equation you will use is
Volume Length Width Height h) Then you
could answer the question by using this
equation Volume of empty space Volume sphere
- Volume cube