Transcript Chapter 10 Notes - Dripping Springs ISD

Chapter 10 Notes
10-1 Area: Parallelograms
Area of a figure is the number of
square units it encloses. The stuff
inside of a figure.
Area of a Parallelogram: product of
any base length b and the
corresponding height h( always makes
a right angle).
A = bh
10-1 Area: Parallelograms
4 ft
6 in
2.5 in
A = bh
= (2.5)(6)
= 15 in2
1 yd
A = bh
= (4)(3) - change 1 yd to
3 feet
= 12 ft2 or 4 yd2
10-2 Area: Triangles and
Trapezoids
Area of a Triangle: A = (bh)/2 or (1/2)bh
h
b
Find area of triangles below:
5m
5.4 m
2m
5 ft
4 ft
1.8 ft
8.2 ft
10-2 Area: Triangles and
Trapezoids-answers
Area of a Triangle: A = (bh)/2 or (1/2)bh
h
b
Find area of triangles below:
A= 7.38 ft2
5m
5.4 m
A= 5 m2
2m
5 ft
4 ft
1.8 ft
8.2 ft
10-2 Area: Triangles and
Trapezoids
Area of a Trapezoid: (1/2)h(b1 + b2) or h(b1 + b2)/2
b2
Find the area of the
following trapezoids:
h
b1
7 in
3 in
3 in
4 cm
5 in
4 cm
7 cm
9 cm
10-2 Area: Triangles and
Trapezoids-answers
Area of a Trapezoid: (1/2)h(b1 + b2) or h(b1 + b2)/2
b2
Find the area of the
following trapezoids:
h
b1
7 in
3 in
4 cm
5 in
4 cm
9 cm
A = 22 cm2
3 in
A = 15 in2
7 cm
10-2 Area: Triangles and
Trapezoids
Find the area of the following figures:
18 ft
12 in
10 ft
10 in
5 ft
20 ft
6 in
4in
10-2 Area: Triangles and
Trapezoids-answers
Find the area of the following figures:
18 ft
12 in
10 ft
10 in
6 in
6 ft
20 ft
A = 234 ft2
A = 108 in2
4in
10-3 Area: Circles
Area of Circle: A = πr2
r
Find Area:
16 m
10 ft
6 mm
12 mm
10 ft
10-3 Area: Circles - answers
Area of Circle: A = πr2
r
Find Area:
16 m
10 ft
6 mm
12 mm
A = 201 m2
10 ft
A = 21.5 ft2
A = 339 mm2
10-4 Space Figures
Space Figures: 3-D figures
Prism - two parallel bases that are
congruent polygons
Pyramid - has a base that is a polygon.
Lateral faces are triangles.
Cylinder - has two parallel bases that are
congruent circles
Cone - one circular base and one vertex
Sphere - a 3-d ball
10-4 Space Figures
Net - an unfolded space figure
10-4 Space Figures-answers
Net - an unfolded space figure
Square prism
Hexagonal pyramid
Pentagonal prism
10-4 Space Figures
10-4 Space Figures-answers
Base = rectangle
Base = pentagon
Rectangular prism
Pentagonal pyramid
Base = circle
cone
Base = hexagons
Hexagonal prism
10-4 Space Figures
10-4 Space Figures-answers
Base = triangles
Base = rectangle
Triangular prism
Rectangular pyramid
10-5 Surface Area: Prisms
 Lateral area: sum of the area of the faces OR
L.A. = ph
 Surface area: sum of all the faces and bases
OR
S.A. = ph + 2B
 p = perimeter of the base
 B = area of the base
 h = height
Surface area of a net
Surface area of a net-answers
3300
ft2
356 m2
1092 in2
SA of Prisms
SA of Prisms-answers
500 in2
480 mm2
10-5 Surface Area of Cylinders
 Lateral area: product of the circumference of
the base and the height OR
L.A. = 2πrh
 Surface area: sum of the lateral area and the
areas of the 2 bases OR
S.A. = 2πrh + 2πr2 or 2πr(h +r)
SA of Cylinders
SA of Cylinders-answers
9470.2 cm2
About 330 cm2
10-6 Surface Area: Pyramids,
Cones, and Spheres
Surface Area of a Pyramid:
o Lateral Area - area of each triangle added
together or the formula: LA = (1/2)Pl or Pl / 2
o Total Surface Area -sum of the area of each
triangle and area of the base or the formula:
Total SA = (1/2)Pl + B
P represents Perimeter of the base of a 3-D figure
B represents Area of the base 3-D figure
l represents slant height
10-6 Surface Area: Pyramids,
Cones, and Spheres
Find lateral area and total surface area.
Lateral Area:
Total Surface Area:
10-6 Surface Area: Pyramids,
Cones, and Spheres-answers
Find lateral area and total surface area.
Lateral Area:
80 m2
Total Surface Area:
80 + 25 = 105 cm2
10-6 Surface Area: Pyramids,
Cones, and Spheres
Find lateral area and total surface area.
Lateral Area:
Total Surface Area:
10-6 Surface Area: Pyramids,
Cones, and Spheres-answers
Find lateral area and total surface area.
Lateral Area:
108 cm2
Total Surface Area:
108 + 36 = 144 cm2
10-6 Surface Area: Pyramids,
Cones, and Spheres
Surface Area of a Cone:
o Lateral Area - area of the sides
LA = πrl
o Total Surface Area -sum of the lateral area
and area of the base:
Total SA = πrl + B or πrl + πr2
10-6 Surface Area: Pyramids,
Cones, and Spheres
Lateral Area:
Total Surface Area:
10-6 Surface Area: Pyramids,
Cones, and Spheres
Lateral Area:
(3.14)(3)(7)= 65.94 m2
Total Surface Area:
65.94 + (3.14)(32) =
94.2 m2
10-6 Surface Area: Pyramids,
Cones, and Spheres
Lateral Area:
Total Surface Area:
10-6 Surface Area: Pyramids,
Cones, and Spheres-answers
Lateral Area:
(3.14)(7)(15)= 329.7 ft2
Total Surface Area:
329.7 + (3.14)(72) =
483.56 ft2
10-6 Surface Area: Pyramids,
Cones, and Spheres
Surface Area of a Sphere:
Total Surface Area = 4πr2
SA =
10-6 Surface Area: Pyramids,
Cones, and Spheres
Surface Area of a Sphere:
Total Surface Area = 4πr2
SA =
200.96 units squared
10-6 Surface Area: Pyramids,
Cones, and Spheres
Find surface area of each figure:
10-6 Surface Area: Pyramids,
Cones, and Spheres-answers
Find surface area of each figure:
216 m2
122 m2
10-7 Volume of Prisms and
Cylinders
 Volume of a prism: product of the area of the base
(B) and the height (h)
 V = Bh

OR
V = lwh (rectangular prism)
V = (bh)H/2 (trianglular prism)
H = height of prism
 Volume of Cylinders: the base area (B) times the
height (h)
 V = Bh
OR
V = πr2h
Answers
628 m3
726
in3
1408 cm3
480
ft3
147,706 in3
25,434 cm3
Answers
8139 m3
192 ft3
10-9 Volume: Pyramids, Cones,
and Spheres
Volume of Cone:
V = (1/3) Bh or Bh/3
B = area of the base
10-9 Volume: Pyramids, Cones,
and Spheres-answers
Volume of Cone:
V = (1/3) Bh or Bh/3
B = area of the base
1272 in3
33 mm3
10-9 Volume: Pyramids, Cones,
and Spheres
Volume of a Pyramid:
V = (1/3) Bh or Bh/3
B = area of the base
10-9 Volume: Pyramids, Cones,
and Spheres-answers
Volume of a Pyramid:
V = (1/3) Bh or Bh/3
33 m3
B = area of the base
1728 in3
10-9 Volume: Pyramids, Cones,
and Spheres
Volume of a Sphere:
V = (4/3) πr3 or (4πr3)/3
B = area of the base
10-9 Volume: Pyramids, Cones,
and Spheres-answers
Volume of a Sphere:
V = (4/3) πr3 or (4πr3)/3
3052 ft3
B = area of the base
5572 cm3
10-9b Scaling and Volume
 Similar solids have the same shape and all
their corresponding dimensions are
proportional.
 The ratio of corresponding edge lengths of 2
similar solids is the similarity ratio.
 Similarity ratio: length of front edge of smaller
length of front edge of larger
Each pair of prisms is similar. Find the similarity ratio and
ratio of the volumes of each.
Each pair of prisms is similar. Find the similarity ratio and
ratio of the volumes of each.-answers
Similarity ratio = 1:2
Ratios of volume = 1:8
Similarity ratio = 2:3
Ratios of volume = 8:27
Each pair of prisms is similar. Find the volume of the larger prism.
Each pair of prisms is similar. Find the volume of the larger prism.
answers
216 ft3
11.4 yd3