Cogito
Grade 7 Math · Chapter 8 · Lesson 2
Volume and Surface Area of Prisms
Base area times height, whatever the base.
10 problems · about 18 minutes · 7.G.B.6
What this lesson teaches
The child finds the volume and surface area of prisms with various bases.
- Volume of a prism is base area times height.
- The base can be any shape.
- Surface area adds the two ends and every side.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Angle Pairs: Supplementary to 47?
Answer 133
Why 133 degrees.
Review — Telling Area from Circumference: Edging a round rug. 1 for circumference, 2 for area.
Answer 1
Why Circumference.
Warm Up
Straightforward practice. Get the method working first.
4 problemsBase area 18, height 7. Volume?
Answer 126
Why 126.
What is the volume of any prism?
Answer Base area times height.
Why Base area × height works for any prism.
Base area 20, height 6. Volume?
Answer 120
Why 20 × 6.
Triangle base 8, triangle height 5. What is the base area?
Answer 20
Why Half of 40.
Build It Up
The same ideas with more to keep track of.
2 problemsBase area 12, height 9. Volume?
Answer 108
Why 12 × 9.
A cube with edge 4. Volume?
Answer 64
Why 16 × 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Tent: A triangular base of area 15 and a length of 8. What is the volume?
Answer 120 cubic units
Why 120.
The Box: A box 6 by 4 by 5. What is the volume?
Answer 120 cubic units
Why 120.