7th Grade Geometry Unit - Slicing 3-d Shapes
DAY 9
Consider a ball 𝐵. Figure 3 shows one possible slice of 𝐵.
a.
b.
c.
What figure does the slicing plane form? You may choose your method of
representation of the slice (e.g., drawing a 2D sketch, a 3D sketch, or describing the
slice in words
Will all slices that pass through 𝐵 be the same size? Explain your reasoning.
Figure 3. A Slice of Ball 𝐵
What do you know about the slice that
would occur right through the middle horizontally? What about vertically?
The right rectangular prism in Figure 4 has been sliced with
a plane parallel to face 𝐴𝐵𝐶𝐷. The resulting slice is a
𝐴
rectangular region that is identical to the parallel
face.
a.
Label the vertices of the rectangular region
defined by the slice as 𝑊𝑋𝑌𝑍.
𝐺
𝐹
𝐷
𝐻
𝐸
𝐶
𝐵
Figure 4.
b.
To which other face is the slice parallel and
identical?
c.
Based on what you know about right rectangular prisms, which faces must the slice be
perpendicular to?
WATCH: Slice a Rectangular Pyramid
https://www.khanacademy.org/math/geometry/basic-geometry/crosssections/v/vertical-slice-of-rectangular-pyramid
DO: Khan Academy PRACTICE : Sling 3D Figures
https://www.khanacademy.org/math/geometry/basic-geometry/crosssections/e/slicing-3d-figures
WATCH: Ways to cut a Cube https://www.khanacademy.org/math/geometry/basicgeometry/cross-sections/v/ways-to-cut-a-cube
DO: Khan Academy PRACTICE: Cross sections of 3D objects
https://www.khanacademy.org/math/geometry/basic-geometry/crosssections/e/cross-sections-of-3d-shapes