Cogito
Geometry · Chapter 8 · Lesson 1
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
What this lesson teaches
The student computes the volume and surface area of the standard solids.
- Prisms and cylinders are base area times height.
- Cones and pyramids are one third of that.
- Scaling by k multiplies area by k² and volume by k³.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
1 problemReview — Proving Things with Coordinates: From (2, 1) to (6, 4). Distance?
Answer 5
Why 5.
Warm Up
Straightforward practice. Get the method working first.
4 problemsBase area 18, height 9. Volume?
Answer 162
Why 162.
A cone is what fraction of the cylinder containing it?
Answer One third.
Why Exactly one third.
Base area 25, height 6. Volume?
Answer 150
Why 25 × 6.
A cylinder has volume 150. A cone with the same base and height?
Answer 50
Why One third.
Build It Up
The same ideas with more to keep track of.
2 problemsA solid scaled by 2. How many times bigger is the volume?
Answer 8
Why 2 cubed.
A solid scaled by 4. How many times bigger is the surface area?
Answer 16
Why 4 squared.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsThe Cylinder: Base area 20, height 7. What is the volume?
Answer 140 cubic units
Why 140.
The Cone: A cylinder has volume 96. A cone with the same base and height?
Answer 32 cubic units
Why 32.
The Scaling: A solid is scaled by 3. How many times bigger is its volume?
Answer 27 times
Why 27 times.