Volume of prisms and cylinders

Three quick questions from earlier lessons.

A stack of identical coins forms a cylinder. If each coin has area $A$ and the stack is $h$ high, what is its volume?

Base area times height.

For any prism or cylinder:

V = B \cdot h

, with

B

the area of the base. Cylinder:

V = \pi r^2 h

.

A cylinder with $r = 3$ , $h = 10$ .

Not to scale

B = 9\pi

Base area.

V = 90\pi \approx 282.7

Times height.

Your turn: a rectangular prism 4 by 5 by 6.

120

4 × 5 × 6.

Find the volume of a cylinder with radius 3 cm and height 4 cm (exact, in terms of π).Not to scale
Find the volume of a cylinder with radius 8 cm and height 11 cm (exact, in terms of π).Not to scale

A prism has a triangular base with base 2 cm and height 7 cm, and the prism is 7 cm long. Find its volume (cm³).Not to scale

A cylinder of radius 5 cm has volume $175\pi$ cm³. Find its height (cm).Not to scale
A cylinder of radius 6 cm has volume $360\pi$ cm³. Find its height (cm).Not to scale

Three questions to check you have got it.

Find the volume of a cylinder with radius 3 cm and height 4 cm (exact, in terms of π).Not to scale
Find the volume of a cylinder with radius 8 cm and height 11 cm (exact, in terms of π).Not to scale
Find the volume of a cylinder with radius 5 cm and height 5 cm (exact, in terms of π).Not to scale

Prisms and cylinders

$V = Bh$ ; cylinder $V = \pi r^2 h$ .

Watch out: base area, not circumference.

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