Three Dimensional Shapes
Find the total surface area of the triangular prism below. 8cm--- side of triangular 10cm--- bottom side of triangle 6cm --- side slide 12cm-- slide
A= 10×6=60 cm^2 B=8×6=48 cm^2 C=12×6=72 cm^2 D=1/2(8×10)=40 cm^2 60+48+72+2(40)= 260 cm^2 Answer: 260 cm^2
Cylinder --- SA
A= 2πrh+2πr^2
Find the total surface area of triangular pyramid below. Length of the base rectangle = 15 unit Width of the base rectangle = 15 unit Height of triangle on the side of pyramid = 15 unit Length of the base of the triangle = 15 unit
Area of base = length × width = 15 × 15 = 225 unit² Area of the triangle = 1/2 × base × height = 1/2 × 15 × 15 = 112.5 unit² Surface Area = 225 + 4 × 112.5 = 675 unit² Answer: 675 unit²
circle
C=2πr A=πr^2
sphere
It has no faces, edges, or vertices
What is the lateral and total surface area of a cylinder with radius 3 inches and height 5 inches?
Lateral Surface Area = 2πh LSA = 2π(3)(5) LSA = 30π ≈ 94.25 in B = πr^2 B = π(3)^2 B = 9π ≈ 28.27 square inches 9π x2 = 18π-----> 30π + 18π= Answer: 48π
triangle
P = sum of all sides A=1/2 bh
Trapezoid
P = sum of all sides A= r 1/2 (b1 + b2)h
Parallelogram
P=2(w+l) A=bh
Rectangle
P=2(w+l) A=l×w
Square
P=4s A=s^2
What is the volume cylinder with a diameter of 8 cm and a height of 6 cm?
Radius = ½ (8) = 4 cm V = π(4)^2 X 6 V = 96π ≈ 301.59 cm^3 Answer: 301.59 cm^3
What is the surface area of a rectangular prism with length 4.5 inches, width 6 inches, and height 8 inches?
SA = 2(6 X 8+4.5) X (6 + 4.5 X 8) SA = 2(48 + 27 + 36) SA = 2(111) SA = 222 in2
Rectangular Prism ----- SA (box)
SA=2(wh+lw+lh)
SA of Sphere
SA=4πr^2
Surface Area of a Cone
SA=πrl+πr²
Prism
quadrilateral faces with two congruent bases (and no apex).
slant height
the height of each lateral face
net
two-dimensional representation or pattern for a three-dimensional object.
Cylinder Volume
πr^2h
Triangular Prism Volume
1/2 X bhl
Cone Volume
1/3πr^2h
Find the total surface area of the rectangular pyramid below. h=8ft bottom of h= 12ft sh=9.5ft bottom of sh= 6ft
12 x 6= 72 (12 X 8)/2= 48 ft (6 X9.5)/2= 28.5 ft 72+ 2(48)+2(28.5)= 225 ft^2 Answer: 225 ft^2
Find the total surface area of the rectangular pyramid below. h= 8ft sh= 9.5ft bottom of h= 12ft bottom of of sh= 6ft
12 x 6= 72 ft 12 x 8/2= 48 ft 6 X 9.5/2= 28.5 ft 72 + 2(48)+ 2(28.5)= 225 ft ^2 Answer: 225 ft ^2
Using the net below, determine the total surface area of the cube. (2cm)--- (cubes)
2X2 = 4cm^2 6X4cm^2 = 24 cm^2 Answer: 24 cm^2
Sphere Volume
4/3πr^3
Rectangular Pyramid ---- SA
Use a net
Triangular Prism---- SA
Use a net
Triangular Pyramid ---SA
Use a net
What is the volume of a sphere with radius 2 inches?
V = 4/3πr^3 V = 4/3π(2)^3 V = 32/3π ≈ 33.51 in3 Answer: 33.51 in^3
What is the volume of a cone that has a height of 5.5 inches and a base with a radius of 3 inches?
V = ⅓πr^2h V = ⅓π(3)^2 X 5.5 V = 16.5π ≈ 51.84 in^3 Answer: 51.84 in^3
Rectangular Pyramid Volume
V= 1/3 Bh
Triangular Pyramid Volume
V= 1/3 Bh
Rectangular Prism Volume
V=lwh
Pentagonal Prism
Vertices 10 Edges 15 Faces 7
Hexagonal prism
Vertices 12 Edges 18 Faces 8
Triangular pyramid
Vertices 4 Edges 6 Faces 4
Quadrangular pyramid
Vertices 5 Edges 8 Faces 5
Square pyramid
Vertices 5 Edges 8 Faces 5
Pentagonal pyramid
Vertices 6 Edges 10 Faces 6
Triangular prism
Vertices 6 Edges 9 Faces 5
Hexagonal pyramid
Vertices 7 Edges 12 Faces 7
Cube
Vertices 8 Edges 12 Faces 6
Quadrangular prism
Vertices 8 Edges 12 Faces 6
Rectangular Prism
Vertices 8 Edges 12 Faces 6
Square prism
Vertices 8 Edges 12 Faces 6
What is the volume of a right rectangular prism with height 5 cm, width 4.5 cm, and length 4 cm?
Volume = l × w × h V = 4 × 4.5 × 5 V = 90 cm3 Answer: V = 90 cm3
irregular prism
a prism that has an irregular polygon as its base
oblique prism
a prism that is not a right prism
right prism
a prism whose lateral faces are all rectangles
regular prism
a prism with bases that are regular polygons
pyramid
a shape in three dimensions that has one polygon for a base and triangular faces that meet at a point
area
amount of surface inside of a figure. square inches (in.2) square miles (mi.2) square centimeters (cm2) square kilometers (km2)
Find the area of the figure below. PENTAGON
bottom rectangle= 6 x 4 = 24 top Triangle = 1/2 X 6 X2= 6 total area- 24+6= 30
perimeter
distance around the outside of that figure. inches (in.) feet (ft.) miles (mi.) centimeters (cm)
pyramid
has a base, triangular faces, and an apex (where the faces meet).
