Transcript Document 7428790

Surface Area and
Volume
At exactly 11:00 (12:30) I will put up
the warm up. At your tables, do as
many as you can in 3 minutes!
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Fill in the blanks with
conversions--no peeking!
16: C ___ in a G ___
32: D ___ F___ at which W ___ F ___
60: M ___ in a(n) H ___
16: O ___ in a P ___
1000: M ___ in a M ___
8: L ___ O ___ in a C ___
2.2: K ___ in a P ___
0.6: M ___ in a K ___
1760: Y ___ in a M ___
1: Q ___ in a L ___
2.54: C in a(n) I ___
Agenda
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Go over warm up
Check HW
Volume of prisms and cylinders
Exploration 10.14
Assign Homework
Hints
• 2a. P: half a circle + 2 legs of the triangle.
Use Pythagorean Theorem.
A: half a circle + area of the triangle.
P = 3π + 6.7 + 6.7 m; A = (9/2)π + 18 m2
• 2b. P: Extend the top horizontal line to form
a right triangle. Use Pythagorean Theorem.
A: area of the rectangle + area of the right
triangle.
P = 11.66 + 60 m; A = 240 + 30 m2
• 5. Find 128/360 of the circumference. 11.16 ft
• 7a. (1) Enclose the figure in a rectangle. Find are of
entire rectangle and subtract the white region.
(2) Draw lines to form 3 rectangles. 175 cm2
• 7b. (1) Enclose the figure in a rectangle. Find are of
entire rectangle and subtract the white region.
(2) Draw in a vertical line to form two trapezoids. (3)
Draw in a horizontal line to form 2 triangles and a
rectangle.
• 9. Draw a square--subdivide the length and
width into 12 1-inch segments. Then, count
the squares that are formed. 144 square
inches
• 10. Find the area of the backyard. How
many full bags are needed to cover the
backyard?
9600 sq. ft to be covered; 10 bags needed;
$39.90
• 11. The shed has area 6 • 10. The new rectangle with the
border is (6 + 2x) • (10 + x). Subtract the area of the shed,
and set the remaining area to 18 square feet. 0.65 ft. (7.8
in.)
• 14. The area of the square is 36 sq. m. So, the length of a
side is ___. Then, the perimeter of the square is ___.
Now, use this amount of fence in a circle--that is, find the
distance around the circle. Determine the radius, and then
find the area of that circle.
Fence = 24 m; radius of circle = 3.82; area =
45.82 m2
• 15. Since the 12-inch diagonal cuts create an
isosceles right triangle, (12, 12, and x), use the
Pythagorean Theorem to find x, the length of the
original square. 16.97 in.
• 20. The radius of the flower bed is 3 m. The radius
of the flower bed plus the sidewalk is
(3 + 1) m. Find the difference in the areas.
16π - 9π = 21.98 m2.
• 26. Think of the work we did in Exploration 10.12.
a. 9 x 1 and 5 x 5 b. 9 x 1 and 4 x 5
c. Same as a.
d. Same as b.
• 29b. Count the “square units” in each region.
Each is 2 sq. un.
• 45. Think of the work we did in Exploration 10.12.
Remember, the figures may be non-convex.
P = 20 un., A = 9 sq. un. P = 20 un., A = 25 sq. un
• 48a. What will it look like if you put all the white
areas together?
25π cm
• 48b and c. How many missing lengths can you find?
b. Need distance between horizontal lines.
c. 34 + 3π in.
• 49a and b. How many missing lengths can you find?
a. 84 sq. ft.
b. Need height of the rectangle.
• 50a. Draw a picture. 24.99 sq. in.
• 50b. Think of Exploration 10.12.
• P of big rectangle is 28 in. So, P of little rectangle is 14
in. 1 x 6, 2 x 5, 3 x 4, etc.
• 50c. Think of Exploration 10.12.
If area is 20 sq. cm, then length of 1 side must be less
than 4.47 cm. P is between 17.88 cm (4.7 x 4.7) and very
large 160.5 cm (40 x .5) and bigger.
• 50d. If the length is double the width, draw a picture of
where the posts must go.
Posts: 19 on horizontal, 8 vertical, not counting the
corners. Area = 180 x 90 = 16,200 sq. ft.
Volume of a Cube
• Take a block. Assume that each edge
measures 1 unit.
• So, the volume of that block is
1 unit3. We also call this a cubic unit.
• Use the blocks to make 2 other cubes.
How many cubic units are needed?
Volume of a cube
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Answer:
1 cubic unit, 8 cubic units, 27 cubic units
Any “cube” will be formed with x3 blocks.
Ex: a cube with an edge that measures 13
units will have volume of 133, or 2179 cubic
units.
Make rectangular prisms
• Make 3 different rectangular prisms, each
with a base of 6 cubes.
• The base must be a rectangle. Why?
• The area of the base remains constant.
Why?
• The only thing that changes is the height.
Why?
• What is the volume (number of cubes) of
each prism? Is this related to the L, W, and
H? If so, how?
Dimensions of
Rectangular Prisms
• Do your prisms look like this?
• 3x2x1
3x2x2
• 3x2x3
3x2x4
Rectangular prisms
• Volume: Volume is defined as area of
the base multiplied by the height.
• Why do we say L • W • H for a
rectangular prism?
height
width
length
Exploration 10.15
• Do 3 and 4.
• Show your work and find each answer.
• In 1 - 2 sentences, describe how to
imagine the solution to someone who is
sight-impaired or blind.
Other 4-sided prisms
• Suppose we had a trapezoidal prism.
• Does the area of the base • height still
make sense? (Hint: what is the base?)
3-sided prism
• What is the base? What is the height?
Other prisms
• Can you find the base and height of
each prism?
What is a prism with a
circular base?
• A cylinder.
• Does area of the
base • height of
the cylinder (prism)
still make sense?
• What is area of the
base • height?
In prisms and cylinders…
• The bases are congruent.
• In a prism, the faces are all rectangles.
• Why aren’t the faces of a cylinder also
rectangles?
Surface Area of a Cube
• In a cube, all six faces are congruent.
• So, to find the surface area of a cube, we
simply need to find the area of one face, and
then multiply it by 6.
• If we don’t have a cube, but we have a
rectangular prism, there are still 6 faces: but
they are not all congruent.
• Front and back, top and bottom, right and
left.
Volume and Surface Area
• Assume that each block has volume
1 unit3. Make 4 different polyhedra,
each containing 12 cubes.
• Do all four have the same volume?
• Do all four have the same surface
area?