CHAPTER
CHAPTER 11
11
C
You will need
Making Solids from
Other Solids
• a ruler
• paper for cutting
• scissors
c GOAL
Combine right prisms, right pyramids, and right cylinders to form other solids.
Learn about the Math
In the previous two lessons you have been working with right
prisms and right pyramids, calculating their surface area and
lateral area. These types of figures are three-dimensional
objects, or solids. When the flat surfaces (faces) of these
figures are polygons, they are called polyhedrons. The
segments that join the faces together are edges, and the
corners are vertices.
You learned earlier that a polyhedron whose bases are
congruent and parallel is a prism, and a prism that has bases
aligned one above the other and has lateral faces that are
rectangles is called a right prism.
The previous lesson defined a pyramid as a polyhedron with
one polygonal base and triangular faces that meet at a vertex
called the apex. A right pyramid is a pyramid with a base that
is a regular polygon, which means each side of the polygon
has the same length.
In Lesson 11.2 you learned about another type of solid known
as a cylinder. A cylinder has two parallel circular bases with
the same radius.
You have also learned how to draw each of these three solids.
These solids (right prisms, right pyramids, and right cylinders)
can be combined to form other solids.
Copyright © 2009 by Nelson Education Ltd.
Reproduction permitted for classrooms
right cylinder
11C Making Solids from Other Solids
1
Maggie is building a diorama to be used as a visual for an oral
book report. She wants to include a model of a small home in
her design. The base of the model home is square, with length
2.00 cm and width 2.00 cm. The sides (not including the roof )
are 2.00 cm high. The roof has a slant height of 1.73 cm and
includes four triangles that come to a single point.
can Maggie build her model home,
? How
and what solids will it include?
A. Draw the square base, with the dimensions given.
B. Sketch the four outside walls of the model home, following
the dimensions given.
C. Sketch the triangular shapes that will form each side of
the roof.
D. Cut these shapes out and tape them together to form
the model.
E. What solid shapes do you see in your model?
F. Sketch your model.
Reflecting
1. What is the name given to the segments that join
together the faces of a solid?
2. What is the name of a figure with two parallel circular
bases, each having the same radius?
3. What is the difference between a right prism and a right
pyramid?
4. What is another name for the corners of a solid object?
2
Nelson Mathematics Secondary Year Two, Cycle One
Reproduction permitted for classrooms
Copyright © 2009 by Nelson Education Ltd.
Work with the Math
Example 1: Combining right prisms, right cylinders,
and right pyramids to create other solids
Sketch a solid that includes a right cylinder, a right prism, and a right pyramid.
Denise’s Solution
A
Checking
B
5. What solids are included in this
sketch?
Practising
6. Complete each of the following
statements with a term that will make
it a true statement.
a) A pyramid is a polyhedron with one
__________ base and triangular
faces that come to a point.
b) The segments that join the faces of
a solid together are ___________.
c) The corners of a solid are called
__________.
d) A prism is a polyhedron whose
bases are __________ and parallel.
Copyright © 2009 by Nelson Education Ltd.
Reproduction permitted for classrooms
11C Making Solids from Other Solids
3
7. List the solids present in each of the
following sketches.
10. How many edges does the following
solid have?
a)
b)
11. How many faces does the following
solid have?
c)
12. How many edges does the following
object have?
8. Sketch one object that includes the
following solids.
• 2 rectangular prisms with height
2 cm, width 1 cm, and depth 2 cm
• right cylinder with diameter 1 cm
and length 2 cm
9. Sketch one object that includes the
following solids.
• rectangular prism with length 2 cm,
width 2 cm, and depth 2 cm
• square pyramid with base 2 cm 3
2 cm and slant height 3 cm
4
Nelson Mathematics Secondary Year Two, Cycle One
Reproduction permitted for classrooms
Copyright © 2009 by Nelson Education Ltd.