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The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone. The formula for the surface area S of a cone is S=πr2+πrl, where r is the radius of the base and l is the slant height. Find the height of the cone.

 

 Sep 13, 2020
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To solve this problem, you actually don't need to know the cone formula! This is simply the Pythagorean Theorem. 

 

Using the theorem, which is  \(a^2+b^2=c^2\) , we can insert our variables into the equation. Since \(c^2\) is the hypotenuse of the triangle, 12 will be our \(c\)

 

\(h^2+6^2=12^2\)

 

\(h^2+36=144\)

 

\(144-36=h^2\)

 

\(h^2=108\)

 

\(h=\sqrt108=6\sqrt3\)

 

So, the height of the cone is \(6\sqrt3\) cm. 

 

Hope this helps!

 

Doggo

 Sep 13, 2020

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