Volume and Surface Area of Prisms and Cylinders
Find the volume of any prism as base area times length, and its surface area as the two ends plus the wrapped rectangle, including the cylinder.
What a learner can do afterwards
- Compute the volume of a triangular prism and of a cylinder from the base area and length
- Find the surface area of a cylinder by separating the two circles from the curved rectangle
- Work backwards from a stated volume to a missing radius or length, keeping units cubed and squared straight
1 · Read
Volume counts the cubes that fit inside. For any prism or cylinder, find the area of one end face, then multiply by the length between the ends. A triangular end has area half base times height. Slant the solid and the volume stays put, since every slice still matches.
A triangular prism has a right-angled end with legs 6 cm and 4 cm, and length 10 cm. The end area is half of 6 times 4, which is 12 square cm. The volume is 12 times 10, which is 120 cubic cm. Run it backwards by dividing: volume divided by end area gives the length.
A closed cylinder unfolds into two circles plus one rectangle that wraps around. The curved area is the circumference times the height. Add both circles and the rectangle for the total surface area.
Check every measurement shares one unit before you multiply. Keep areas in square units and volumes in cubic units. Finish by asking if the answer is sane: a thin long prism cannot hold litres.
Volume is end area stretched along the length, surface area is every face added, and matching cubic and square units keeps both honest.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.