Expressions, equations & relationships · TEKS 7.8A, 7.8B, 7.9A
Volume of prisms & pyramids
Volume is the space inside a 3-D figure. A prism is base area × height. A pyramid is one third of that.
Key steps
- Prism: V = Bh, where B is the area of the base.
- Rectangular base: B = l × w. Triangular base: B = ½ × b × h.
- Pyramid: V = ⅓Bh.
- Same base and height: pyramid = prism ÷ 3.
Worked example
Square pyramid: base 6 m × 6 m, height 10 m. Volume?
- B = 36 m².
- V = ⅓ × 36 × 10 = 120 m³.
- Answer: 120 m³
Watch out: Two different "heights" appear with triangular prisms: the triangle’s height (for B) and the prism’s length. Use each in its place.
Practice
5 questions with new numbers every set. Get 4 of 5 to mark this topic as practiced.