Before you read

Answer first — see what you already know.

A shipping crate has interior dimensions of 8 cm $\times$ 5 cm $\times$ 3 cm. What is the volume of goods it can hold?

Check your answer

Answer:

Before you read

Answer first — see what you already know.

A cylindrical water tank has a diameter of 10 inches and a height of 7 inches. What is its volume?

Check your answer

Answer:

Theory

Volume Formulas

Rectangular prism (box): $V = lwh$

Cube: $V = s^3$

Cylinder: $V = \pi r^2 h$

Cylinder: V = πr²h

Cone: $V = \frac{1}{3}\pi r^2 h$

Cone: V = ⅓πr²h

Sphere: $V = \frac{4}{3}\pi r^3$

Sphere: V = ⁴⁄₃πr³

Pyramid: $V = \frac{1}{3}Bh$ (where $B$ = area of base)

Notice the pattern: a cone is $\frac{1}{3}$ of a cylinder, and a pyramid is $\frac{1}{3}$ of a prism.

Example 1

A cylinder has radius 5 cm and height 10 cm. What is its volume?

$V = \pi(5)^2(10) = 250\pi \approx 785.4$ cm $^{3}$

250\pi \approx 785.4

^{3}

Example 2

A cone has the same dimensions. What is its volume?

$V = \frac{1}{3}\pi(5)^2(10) = \frac{250\pi}{3} \approx 261.8$ cm $^{3}$

\frac{250\pi}{3} \approx 261.8

^{3}

Common Mistakes

Common Mistakes to Avoid

Radius vs. diameter

Always check if the problem gives you the radius or the diameter. If diameter, divide by 2!

Remember: radius vs. diameter — Always check if the problem gives you the radius or the diameter. If diameter, d...

Forgetting the

\frac{1}{3}

Cones and pyramids use $\frac{1}{3}$ of the corresponding prism/cylinder formula.

Remember: forgetting the

\frac{1}{3}

— Cones and pyramids use

\frac{1}{3}

of the corresponding prism/cylinder formula...

Cubing vs. squaring

Sphere volume uses $r^3$ , not $r^2$ .

Remember: avoid this error.

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