GEOMETRY
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name________________________
M3
Period: _____Date______________
Lesson 2: Common 3-Dimensional Shapes and Their Cross- Sections
Learning Target: I can understand the definitions of a general prism and a cylinder and the distinction
between a cross-section and a slice.
Warm Up
Geo CC Regents 201508 11: Linda is designing a circular piece of stained glass with a diameter of 7 inches.
She is going to sketch a square inside the circular region. To the nearest tenth of an inch, find the largest
possible length of a side of the square.
Definition of Prism


A general prism is cylinder in which two bases are equal polygons in parallel planes, and all other
faces are parallelograms.
There are two types of prism; oblique prism and right prism.
Oblique prism is when the axis is not ________________ to the base.
Right prism if the axis is ___________________ to the base.
In right prism, all lateral areas are _____________________.
GEOMETRY
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name________________________
Period: _____Date______________
Terms
Definitions
Base
(Base Face)
The two congruent, parallel sides of a prism
Edge
Vertex
Lateral faces
Slice
Cross Section
M3
Drawing
A segment that is formed By the intersection
Of two faces of a solid.
A point where three or more edges of
A solid intersect.
The faces in a geometric solid that are not the
bases.
A general intersection a plane and a solid.
When the slice is parallel to the base.
Definition of Cylinder
A General Cylinder is 3 dimensional solid in which two faces are parallel bases and the lateral area is in the shape of a
rectangle.
________________ cylinder: A general cylinder whose lateral edges are _____________________ to a circular base
________________ cylinder: A general cylinder whose lateral edges are not _____________________ to a circular base
GEOMETRY
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name________________________
Example 1. Sketch the cross-section of the cylinder below
M3
Period: _____Date______________
Example 2.Sketch the figures formed if the
rectangular regions are rotated around the
provided axis
A pyramid is a solid figure that has a polygon base and the lateral faces are all triangles that meet at a point
Rectangular pyramid is a pyramid with a rectangular base
General cone is solid figure with a circular base and a single vertex.
Example 3. Sketch the cross-section of the cylinder below
Example 4. Sketch the figures formed if the rectangular
regions are rotated around
GEOMETRY
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name________________________
M3
Period: _____Date______________
Spheres and Hemispheres
Every point on the sphere, is the same distance from the origin in space
The cross-section of a sphere is always a ______________
Each half of a sphere is called a Hemisphere
3-D Solids
1. A regular pyramid with a
square base
2. A wooden cube
3. A cone
4. An oblique cylinder
5. An oblique cylinder
Sketch each figure
Sketch the Cross-section
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name________________________
Lesson 2
M3
Period: _____Date______________
6. Water tower in the
shape of a cylinder
7. Triangular prism
8. Rectangular prism
9. Hemisphere tank
Example 6. Ann buys a block of clay for a Geometry project. The block is shaped like a cylinder with a base area of
48𝜋 𝑐𝑚2 , and the height is three times the radius. Ann decides to cut the block of clay into two pieces. She places a
wire across the diameter of the circular base as shown in the figure. Then, she pulls the wire straight down to create 2
congruent chunks of clay.
Ann wants to keep one chunk of clay for later use. To keep that chunk from drying out, she wants to place a piece of
plastic sheeting on the surface she exposed when she cut through the cylinder.
Describe the newly exposed two-dimensional cross section, and find its area. Round your answer to the nearest
whole square inch. Show your work.
GEOMETRY
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name________________________
M3
Period: _____Date______________
Lesson 2: Common 3-Dimensional Shapes and Their Cross- Sections
Problem Set
1. Sketch the cross-section for the following figures:
a.
b.
c.
d.
2. Draw the cross-section or the slice
a.
b.
c.
3. Sketch the figures formed if the rectangular regions are rotated around the provided axis
a.
b.
GEOMETRY
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
Name________________________
M3
Period: _____Date______________
4. Draw the cross-section or the slice
a.
b.
c.
5. Which figure can have the same cross section as a sphere?
PARCC-type question:
6. Rick buys a block of clay for a Geometry project. The block is shaped like a rectangular prism with
length edges of 12 in, width edges of 6 in, and height edges of 5 in. Rick decides to cut the block of clay
into two pieces. He places a wire across the diagonal of the front face of the prism as shown in the
figure. Then, he pulls the wire straight back to create 2 congruent chunks of clay.
Rick wants to keep one chunk of clay for later use. To keep that chunk from drying out, he wants to place
a piece of plastic sheeting on the surface he exposed when he cut through the prism.
Describe the newly exposed two-dimensional cross section, and find its area. Round your answer to the
nearest whole square inch. Show your work.