Video: Finding the Slant Height of a Cone given Its Height and Its Base Radius

Find the slant height of the figure below.


Video Transcript

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.

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