A pyramid or cone holds exactly a third of the prism or cylinder it fits inside. That one third is the whole difference, and it is the thing people forget.
Not quite the one you need? Same words, different skill:
Dropping the one third. Without it you have found the volume of the prism or cylinder around the shape, which is three times too much.
Also called surface area of a pyramid or slant height.
What you can put on this worksheet
Volume of a cone
A cone has radius 16 and height 30. Find its volume.→ 2560π
Surface area of a cone
Find the exact surface area of the cone. — a cone with radius 16 and slant height 34→ 800π
Volume of a pyramid
The base is a square. Find the volume. — a square pyramid with base edge 8 and height 9→ 192
Pentagonal and hexagonal pyramids
Find the volume. The base is a regular hexagon. — a regular hexagonal pyramid, labeled 8, 6.9, h = 5→ 276
The height from the slant height first
A cone has radius 21 and slant height 29. Find its volume. Leave the answer in terms of π.→ 2940π
Pyramids with a rectangle or triangle base
A pyramid has height 3, and its base is a right triangle with legs 6and 7. Find the volume.→ 21
Questions about these worksheets
Yes. Every volume of pyramids and cones sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the volume of pyramids and cones questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 6: volume of a cone, surface area of a cone, volume of a pyramid, pentagonal and hexagonal pyramids, the height from the slant height first and pyramids with a rectangle or triangle base. Tick as many as you want and set how many of each, or let it spread them evenly.
Dropping the one third. Without it you have found the volume of the prism or cylinder around the shape, which is three times too much.