Find the slant height of the figure below.
If we let the length of the slant height equal 𝑥, we can see that we’ve created a right-angled triangle. In order to calculate the missing length or side of a right-angled triangle, we can use Pythagoras’s theorem. 𝑎 squared plus 𝑏 squared equals 𝑐 squared, where 𝑐 is the hypotenuse or longest side of the triangle, in this case 𝑥.
Substituting in the values from the diagram gives us 𝑥 squared equals six squared plus 11 squared. Six squared is equal to 36. And 11 squared is equal to 121. This means that 𝑥 squared is equal to 157. Square rooting both sides of this equation gives us 𝑥 equals square root of 157.
Therefore, the slant height of a cone with radius six centimeters and height 11 centimeters is the root of 157 centimeters. This is equal to 12.53 centimeters, to two decimal places.