---
title: "Volume and Surface Area of Prisms and Cylinders"
description: "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."
canonical: https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-prisms-and-cylinders-mt_JTLJ5LDrYh
source: https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-prisms-and-cylinders-mt_JTLJ5LDrYh.md
retrieved: 2026-09-12
---

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# 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.

Subject: Mathematics · Area: Geometry · Ages 14 to 15
Page: https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-prisms-and-cylinders-mt_JTLJ5LDrYh

## Ready when they can

- 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

## Lesson: Prisms: base area times length

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.

**Example.** 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.

**Example.** 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.

**Tip.** 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.

**Recap.** Volume is end area stretched along the length, surface area is every face added, and matching cubic and square units keeps both honest.

## Practice

14 questions on this page, each with its working shown.

## Needs first

- [Volume as additive](https://lightmysky.com/learn/mathematics/volume-as-additive-mt_5TBUFnCy5-)
- [Surface Area of Solids](https://lightmysky.com/learn/mathematics/surface-area-of-solids-mt_hdhmurUndc)
- [Volume of cuboids](https://lightmysky.com/learn/mathematics/volume-of-cuboids-mt_nTL-owFJTF)
- [Circles: Circumference & Area](https://lightmysky.com/learn/mathematics/circles-circumference-and-area-mt_svFa6_mjO_)

## Opens up

- [Volume and Surface Area of Cones, Spheres and Pyramids](https://lightmysky.com/learn/mathematics/volume-and-surface-area-of-cones-spheres-and-pyramids-mt_s4K5YMBSzG)
- [Similar Shapes: Area and Volume Scale Factors](https://lightmysky.com/learn/mathematics/similar-shapes-area-and-volume-scale-factors-mt_v37c_AeLQa)