Finding the surface area of cones is not that hard. But it can require some patience and ingenuity, depending on what information is available at the beginning of the problem. Below are some suggested steps to keep track of everything.
Step 1
Identify the radius of the cone's base circle. If you have the diameter, cut it in half to get the radius. If you have the slant height and perpendicular height, use the Pythagorean theorem (see "Tips" below).
Step 2
Write the radius somewhere off to the side, where it's labelled and easy to find, because you will need it several times in several different calculations.
Step 3
Find the area of the base circle by squaring the radius and multiplying by pi.
- If the instructions say anything like "exact value", it means that you write the Greek letter for pi and leave it. So a radius of 3 gives an area of 9pi.
- Otherwise, use 3.14 or your calculator's pi button to finish the multiplication and get a decimal version for the area.
- You can round, but keep at least 3 digits after the decimal point for now.
Step 4
Write that answer off to one side, somewhere where it is labelled "base area" and easy to find.
Step 5
Identify the slant height of the cone. This refers to the height along the slanted side of the cone, not the height from the tip of the cone to the center of the circle.
- The radius, the perpendicular height (from tip to center), and the slant height are related by the Pythagorean theorem. See the "tips" section below.
Step 6
Multiply the slant height times the radius times pi. Again, "exact value" means write pi as pi; otherwise, use 3.14 to get the decimal approximation.
Step 7
Write that answer off to one side, somewhere where it is labelled "lateral area" and easy to find.
Step 8
Add the "base area" from step 4 with the "lateral area" from step 7.
Step 9
Round, as needed. This is your final answer.
Tips
- General rounding rules: any answer under 20 needs at least 2 decimal places. Any answer between 20 and 100 needs only 1 decimal place. Any answer over 100 can be rounded to the nearest whole number.
- The Pythagorean theorem applies to the radius, perpendicular height, and slant height, with the slant height acting as the hypotenuse: (radius) + (perp. height) = (slant height)
Warnings
- If either your radius or your slant height has a square root, you will not be able to finish the addition on step 8.
