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PEAZIT Aha card

A cuboid has three pairs of opposite faces

Volume stacks layers. The surface has two rectangles ab, two ac and two bc.

Dimensions 2, 3 and 4 cm: volume 24 cm³, surface area 52 cm².

Relation	Meaning
V = a × b × c	Multiply all three dimensions.
S = 2(ab + ac + bc)	Add three different face areas and double.
a = 2; b = 3; c = 4: V = 24; S = 52	Units distinguish interior space from covering.

One worked example

V = a × b × cMultiply all three dimensions.
S = 2(ab + ac + bc)Add three different face areas and double.
a = 2; b = 3; c = 4: V = 24; S = 52Units distinguish interior space from covering.

Watch out: The surface formula assumes a closed cuboid with all six faces. An open box has fewer faces.

Goal, prerequisites and card origin

What you will learn: Calculate a rectangular box's volume and surface area.

What you need first: Rectangle area.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

Show connections

Length, area and volume

Length: one dimension — two perpendicular unit lengths form a — Unit square

Unit square — count squares covering the surface — Area: covering a surface

Length: one dimension — three perpendicular unit lengths form a — Unit cube

Unit cube — count cubes filling the space — Volume: filling space

Area: covering a surface — base area × height for a cuboid — Volume: filling space

Volume stacks layers. The surface has two rectangles ab, two ac and two bc.

Without JavaScript, write your answer elsewhere before opening the solution.A cuboid measures 3, 4 and 5 cm. What is its volume in cm³? Enter a number.

Solution — open after your own attempt

60 3 × 4 × 5 = 60 cm³.

A question for your next return: What is the surface area of a closed 3 by 4 by 5 cm cuboid in cm²? Enter a number.

Solution — open after your own attempt

94 2 × (12 + 15 + 20) = 94 cm².

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