SOLUTION: How to find height of a cone when we know Surface area and radius radius is 4 SA 258cm2

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Question 988867: How to find height of a cone when we know
Surface area and radius radius is 4 SA 258cm2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Total surface area of a cone:
A++=+pi%2Ar%28r+%2B+sqrt%28r%5E2+%2B+h%5E2%29%29
if r=4cm and A=258cm%5E2, then
258+=+3.14%2A4%284+%2B+sqrt%284%5E2+%2B+h%5E2%29%29
258+=+12.56%284+%2B+sqrt%2816+%2B+h%5E2%29%29
258+=+50.24+%2B+12.56sqrt%2816+%2B+h%5E2%29
258+-50.24+=+12.56sqrt%2816+%2B+h%5E2%29
207.76=+12.56sqrt%2816+%2B+h%5E2%29
207.76%2F12.56=sqrt%2816+%2B+h%5E2%29
20776%2F1256=sqrt%2816%2B+h%5E2%29
16.54=sqrt%2816+%2B+h%5E2%29
%2816.54%29%5E2=%28sqrt%2816+%2B+h%5E2%29%29%5E2
273.5716=16+%2B+h%5E2
273.5716-16+=h%5E2
257.5716=h%5E2
h=sqrt%28257.5716%29
h+=+16.04
so, the height is 16.04cm