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Cogito

Geometry · Chapter 8 · Lesson 3

Practice Worksheet

Cross Sections and Cavalieri

Slicing a solid, and why a leaning stack holds its volume.

11 problems · about 23 minutes · G-GMD.A.1, G-GMD.B.4

NameDate

Figure — use these to answer the problems

A cylinder. A horizontal slice through it is a circle at every height.

Cylinder

Flat faces

2

Does it roll?

Yes

Turn it0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. A sphere sliced any way. How many sides? Use 0 for a curve.

    Answer

  2. A cube sliced parallel to a face. How many sides has the cross section?

    Answer

  3. A sphere sliced any way. How many sides? Use 0 for a curve.

    Answer

  4. A cone sliced horizontally. How many sides? Use 0 for a curve.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Does leaning a stack change its volume? 1 for yes, 0 for no.

    Answer

  2. Match each solid to the cross section of a horizontal slice.

    Draw a line from each item on the left to its match on the right.

    • Cylinder
    • Cube
    • Triangular prism
    • Circle
    • Square
    • Triangle

  3. A cylinder sliced at a slant. Circle or ellipse? 1 for circle, 2 for ellipse.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Cavalieri needs the two solids to share what? 1 for height, 2 for weight.

    Answer

  2. Two prisms, same base area and height. Same volume? 1 for yes, 0 for no.

    Answer

  3. The Slice

    A cylinder sliced horizontally. How many sides has the cross section? Use 0 for a curve.

    Answer

  4. The Lean

    A leaning prism and an upright one, same height and cross sections. Same volume? 1 for yes, 0 for no.

    Answer