The curved part of a cone opens out into a sector, and its area works out as pi times the radius times the slant height. Add the base circle and you have the whole surface.
Not quite the one you need? Same words, different skill:
Find the surface area of a cone with radius 3 and slant height 5
The base circle is 9 pi.
The curved part is pi times 3 times 5, which is 15 pi.
The answer is 24π.
Where students go wrong
Using the vertical height where the slant height belongs. If you have been given the height, Pythagoras gives you the slant first.
Also called cone surface area or lateral area of a cone.
What you can put on this worksheet
Surface area of a cone
Find the exact surface area of the cone. — a cone with radius 16 and slant height 34→ 800π
When the height is given
A cone has radius 48 and height 14. Find its lateral surface area. Leave the answer in terms of π.→ 2400π
Questions about these worksheets
Yes. Every surface area of a cone 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 surface area of a cone 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 two 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 2: surface area of a cone and when the height is given. Tick as many as you want and set how many of each, or let it spread them evenly.
Using the vertical height where the slant height belongs. If you have been given the height, Pythagoras gives you the slant first.