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

Find the slant height of the figure below.

01:19

Video Transcript

Find the slant height of the figure below.

If we let the length of the slant height equal ๐‘ฅ, we can see that weโ€™ve created a right-angled triangle. In order to calculate the missing length or side of a right-angled triangle, we can use Pythagorasโ€™s theorem. ๐‘Ž squared plus ๐‘ squared equals ๐‘ squared, where ๐‘ is the hypotenuse or longest side of the triangle, in this case ๐‘ฅ.

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