GEOMETRY - CHAPTER 11 STUDY GUIDE
Sec 11.1
A.
Space Figures and Cross Sections
Definition:
Polyhedron (polyhedra)
Draw a polyhedron and label its faces, edges, and
vertices.
Net of a solid:
Draw a cube and a net for a cube.
Cross section:
Draw a cylinder and two different cross sections of the
cylinder.
B.
Prism
C.
Types of Solids: (Draw an example of each type.)
Pyramid
Cone
Cylinder
Sphere
Euler’s Theorem: (pg 599)
The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula _____
Geometry Study Guide – Ch. 11 – 2010
pg 1 of 10
Sec 11.2
A.
Surface Area of Prisms and Cylinders
Definition, formula & drawing:
Prism
Draw a prism and identify the bases, lateral faces, and
altitude/height.
Right Prism
Oblique Prism
Surface area
Ex: Draw a net, then find the surface area and lateral area of the
following prism.
3
Lateral Area
Cylinder
Geometry Study Guide – Ch. 11 – 2010
4
6
Draw a cylinder and its net. Find formulas for the surface area
and the lateral area.
pg 2 of 10
More practice:
Draw a net for each figure. Find the surface area and the lateral area
1.
5 cm
4 cm
7 cm
2.
5 cm
2 cm
3.
7 cm
3 cm
4.
Note: The hexagon is regular.
7 cm
4.
2 cm
Geometry Study Guide – Ch. 11 – 2010
pg 3 of 10
Sec 11.3
A.
Surface Area of Pyramids & Cones
Definition & Drawing:
Pyramid
Draw a pyramid and identify the vertex, base, a base
edge, a lateral face, a lateral edge and altitude/height,
slant height.
Regular Pyramid
Cone
Draw a cone, its net, and write a formula for the surface
area and lateral area.
Examples:
Find the surface area and lateral area of the following pyramids or cones:
1. Square pyramid
2.
8 cm
5 cm
Geometry Study Guide – Ch. 11 – 2010
pg 4 of 10
3. The original height of the pyramid built for Khafre was about 471 ft. Each side
of its square base was about 708 ft. What is the lateral area to the nearest square
foot?
4. Find the surface area of the following figure.
4 cm
10 cm
5 cm
5. Height of the cone = Height of the cylinder = 7 cm, radius of circular base = 3
cm. Find the surface area of the figure.
Geometry Study Guide – Ch. 11 – 2010
pg 5 of 10
Sec 11.4
A.
Volume of a solid:
B.
Formulas for Volume:
Cubes:
Volume of Prisms and Cylinders
Rectangular Prism
Any Prism:
Cylinder:
Cavalier’s principle:
Examples:
Find the volume of the following prisms or cylinders.
1.
5 cm
4 cm
7 cm
Geometry Study Guide – Ch. 11 – 2010
pg 6 of 10
2.
2 cm
5 cm
3.
7 cm
3 cm
4. The volume of a cube is 100 cm3. Find the length of its side.
5. The volume of a cylinder is 50 in3. Its height is twice its radius. Find the radius.
2. A cylindrical hole is drilled through a solid hexagonal prism as shown. Find the volume and surface area
of the remaining solid.
3 cm
2 cm
4 cm
Geometry Study Guide – Ch. 11 – 2010
pg 7 of 10
Sec 11.5
A.
Volume of Pyramids & Cones
Formulas for Volume
Pyramid:
Cone:
Examples:
Find the volume of the pyramid or cone.
1. Square pyramid
2.
5 cm
7 cm
3 cm
3 cm
3. Find the volume of the following
figure.
4. Height of the cone = Height of the
cylinder = 7 cm, radius of circular base =
3 cm. Find the total volume of the
figure.
4 cm
10 cm
5 cm
Geometry Study Guide – Ch. 11 – 2010
pg 8 of 10
Sec 11.6
A.
Surface Area and Volume of Spheres
Formulas for
Surface area of a Sphere:
Volume of a Sphere:
Examples:
1. Find the volume and surface area of a sphere with radius 3 inches.
2. The surface area of a sphere is 100 cm2. Find the radius.
3. The volume of a sphere is 20 in3. Find its radius.
4. Mrs. Vu has a paper cone with radius 1.5 inches and height 4 inches. On it, there is an ice-cream scoop
shaped as a sphere with radius 2 inches.
a) If the ice-cream completely melts into the cone, will it fill the cone? Why or why not?
b) How much paper is needed to make the cone? Show work.
Geometry Study Guide – Ch. 11 – 2010
pg 9 of 10
Sec 11.7
Similar Solids
A.
Investigation:
1) Draw a rectangular prism with dimensions 1 x 2 x 3. Find its surface area and volume.
2) Double each side of the prism. Find its new surface area and volume. Compare the results
to #1.
3) Triple each side of the prism. Find its new surface area and volume. Compare the results to
#1.
4) Draw two cylinders, one with radius 2 cm and height 3 cm, one with radius 3 cm and height
4.5 cm. Find the surface area and volume for each cylinder. What is the ratio of the areas?
Ratio of volumes?
Theorem: Areas and volume of similar solids
If two similar solids have a similarity ratio/scale factor of a:b, then corresponding
areas have a ratio __________, and corresponding volumes have a ratio ____________.
Ex: The similarity ratio of two similar solids is 2:5. If the larger solid has a surface area of 120
cm2 and a volume of 100 cm3, what are the surface area and volume of the smaller solid?
Geometry Study Guide – Ch. 11 – 2010
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