How to Find the Volume and Surface Area of a Cube

Geometry · Volume and surface area

How to Find the Volume and Surface Area of a Cube

Problem

s = 4

Answer

V = 64,\quad SA = 96

Volume measures the space inside a solid. Surface area measures the total area of its faces. For a cube both formulas use only the side length.

Step-by-step solution

Write the volume formula.
$V = s^3$
Why: The volume of a cube is the side multiplied by itself three times.
Substitute the side and cube it.
$V = 4^3 = 64$
Why: Four cubed is 4 times 4 times 4.
Write the surface area formula.
$SA = 6s^2$
Why: A cube has six identical square faces, each with area s squared.
Substitute the side and square it.
$SA = 6(4)^2 = 6 \cdot 16 = 96$
Why: One face has area 16, and there are six faces.

Common mistakes

Using 6s instead of 6s^2 for the surface area.
Using s^4 for the volume. Volume cubes the side.
Mixing units. Volume uses cubic units and area uses square units.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$s = 3$

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$V = 27,\ SA = 54$
$s = 5$

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$V = 125,\ SA = 150$
$s = 2$

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$V = 8,\ SA = 24$
$s = 6$

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$V = 216,\ SA = 216$
$s = 10$

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$V = 1000,\ SA = 600$