### Video Transcript

Find the slant height of the figure below.

If we let the length of the slant height equal ๐ฅ, we can see that weโve created a right-angled triangle. In order to calculate the missing length or side of a right-angled triangle, we can use Pythagorasโs theorem. ๐ squared plus ๐ squared equals ๐ squared, where ๐ is the hypotenuse or longest side of the triangle, in this case ๐ฅ.

Substituting in the values from the diagram gives us ๐ฅ squared equals six squared plus 11 squared. Six squared is equal to 36. And 11 squared is equal to 121. This means that ๐ฅ squared is equal to 157. Square rooting both sides of this equation gives us ๐ฅ 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.