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Cogito

Geometry · Chapter 8 · Lesson 1

Practice Worksheet

Solids and Their Volumes

Prisms, pyramids, cylinders, cones, and spheres.

10 problems · about 21 minutes · G-GMD.A.1, G-GMD.A.3, G-MG.A.1

NameDate

Figure — use these to answer the problems

The tinted base repeats for every layer of height.
  • Cubes in one layer4 × 3 = 12
  • Layers3
  • 4 × 3 × 336 cubic units
Length4
Width3
Height3
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

1 problem

  1. From “Proving Things with Coordinates”

    From (2, 1) to (6, 4). Distance?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Base area 18, height 9. Volume?

    Answer

  2. A cone is what fraction of the cylinder containing it?

    • One third.
    • One half.

  3. Base area 25, height 6. Volume?

    Answer

  4. A cylinder has volume 150. A cone with the same base and height?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. A solid scaled by 2. How many times bigger is the volume?

    Answer

  2. A solid scaled by 4. How many times bigger is the surface area?

    Answer

Stretch Yourself

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

3 problems

  1. The Cylinder

    Base area 20, height 7. What is the volume?

    Answercubic units

  2. The Cone

    A cylinder has volume 96. A cone with the same base and height?

    Answercubic units

  3. The Scaling

    A solid is scaled by 3. How many times bigger is its volume?

    Answertimes