L6 · Volume of Right Prisms and Pyramids

Learning goal

“I can find the volume of any right prism as V = (area of base) x (length), and the volume of a right pyramid with the same base and height as exactly one third of it - V = 1/3 x (area of base) x (vertical height) - and work backwards from a volume to a missing dimension.”

Volume — the space a solid occupies (or holds), in CUBIC units (cm3, m3, ft3). It answers "how much fits inside?"

Base area (B) — the area of the prism's or pyramid's base polygon, the starting point of every volume formula in this lesson.

Vertical height (of a pyramid) — the straight-down distance from apex to base, through the inside. Volume uses THIS height - the slant height returns to its surface-area job only.

One-third relationship — a pyramid holds exactly 1/3 of a prism with the same base and height; a cone holds exactly 1/3 of its cylinder (Lesson L7). Indicator 3.6 in action.

Worked example

Sketch and label first. A right triangular prism has a triangular base with base 6 cm and height 4 cm; the prism is 10 cm long. Find its volume. Step 1: Base area: B = 1/2 x 6 x 4 = 12 cm2. Step 2: V = B x length = 12 x 10 = 120 cm3. For a rectangular prism this is the familiar l x w x h wearing its general form: B = l x w, then x h.

Check yourself — explain it

Why does the prism formula multiply the base area by the length?

Paired problem — example still visible

Rectangular prism 8 cm by 3 cm by 5 cm -> B = 24; V = 24 x 5 = 120 cm3

Faded completion — last step is yours

"Triangular prism: triangle base 8 cm, triangle height 5 cm, length 7 cm. B = 1/2 x 8 x 5 = 20 cm2; V = 20 x 7 = ___ cm3" -> 140 cm3

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz

Grade 10 — Mathematics 10C › C10U02 Surface Area & Volume

L6 · Volume of Right Prisms and Pyramids