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Find the slant height of the figure below.
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If we let the length of the slant height equal ๐ฅ, we can see that weโve created a right-angled triangle.
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In order to calculate the missing length or side of a right-angled triangle, we can use Pythagorasโs theorem.
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๐ squared plus ๐ squared equals ๐ squared, where ๐ is the hypotenuse or longest side of the triangle, in this case ๐ฅ.
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Substituting in the values from the diagram gives us ๐ฅ squared equals six squared plus 11 squared.
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Six squared is equal to 36.
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And 11 squared is equal to 121.
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This means that ๐ฅ squared is equal to 157.
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Square rooting both sides of this equation gives us ๐ฅ equals square root of 157.
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Therefore, the slant height of a cone with radius six centimeters and height 11 centimeters is the root of 157 centimeters.
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This is equal to 12.53 centimeters, to two decimal places.