L6 · Volume of a right rectangular prism

Learning goal

“I can find the volume of a right rectangular prism by multiplying the area of its base by its height (V = l x w x h) - and I can explain why the formula works with layers.”

Right rectangular prism — a box shape with rectangle faces and square corners everywhere (the "right" means the sides go straight up from the base).

Base area — the area of the bottom face, in square units (cm2 or m2).

Height (of a prism) — how many layers tall the prism is; the distance from the base to the top face.

Volume formula — V = base area x height, which is the same as V = length x width x height.

Worked example

A box is 5 cm long, 3 cm wide, and 4 cm high. Step 1: The base is a 5 x 3 rectangle. Its area is 5 x 3 = 15 cm2 - so one layer holds 15 cubes. Step 2: The height is 4, so there are 4 layers: 15 x 4 = 60 cubes. Step 3: V = length x width x height = 5 x 3 x 4 = 60 cm3. Say it plainly: base area x height is the layers count from L5, written as a formula.

Check yourself — explain it

Why do we multiply the base area by the height?

Paired problem — example still visible

A prism 6 cm x 2 cm x 3 cm. -> Base area 6 x 2 = 12; V = 12 x 3 = 36 cm3

Faded completion — last step is yours

"Base 7 cm x 2 cm, height 5 cm: base area = ___ cm2; V = ___ x 5 = ___ cm3" -> 14 cm2; 14; 70 cm3

Ready to practise?

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

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