Part 05 · Angles and area · Card 7 of 8
Volume of prisms and cylinders
A prism has the same shape all the way through. Its volume is the area of the cross-section times the length.
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Analogy
Like stacking identical slices of bread to make a loaf.
Example
Cylinder r = 3, h = 10
Cross-section = pi x 3^2 = 9 x piVolume = 9 x pi x 10= 90 x pi = 282.7 cubic units
In practice
Water tanks and tins are prisms or cylinders, so volume tells you how much they hold.
Practice
Flashcards
- What is the volume of a prism?Area of the cross-section times the length.
Interview questions
- A cylinder has radius 3 cm and height 10 cm. Find its volume.
- Area of the circle end = pi x 3^2
- That is 9 x pi, about 28.3 cm^2
- Multiply by the height 10
- Volume is about 282.7 cm^3
Questions people ask
What is the formula for volume of a cylinder?
Volume = pi x r^2 x h. The first part, pi x r^2, is the area of the circular end. Multiply by the height to find the volume. A cylinder with radius 3 and height 10 has volume 90 x pi, which is about 282.7.
Why are volumes in cubic units?
Volume counts how many unit cubes fit inside a solid, so you multiply three lengths. The units are cubed: cm^3 or m^3. A box 2 cm by 3 cm by 4 cm has a volume of 24 cm^3. Capacity uses the same idea.