The radius of a cone - Math Central

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Question from lee, a student:

hi
i have a cone to calculate, the height and radius are equal and the slant height is 0.5m

the total surface area is 15m sq i need to calculate the radius of the cone Note : this will lead to a quadratic equation could somebody have a look please
Thanks
Lee

Hi Lee,

There is something incorrect in this problem. If the height h and radius r are equal then the situation you have is

cone

Since triangle PQR is a right triangle, Pythagoras' theorem tells us that

h² + r² = 0.5²

But r = h so

2 r² = 0.5² or r² = 0.125 and r = 0.35 meters

Penny

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