SOLUTION: The surface area of a closed cone of height h and base radius r is given by A = πr² + πr√(h² + r²). Show that h = (A/πr)√(1 - (2πr²/A))

Algebra ->  Surface-area -> SOLUTION: The surface area of a closed cone of height h and base radius r is given by A = πr² + πr√(h² + r²). Show that h = (A/πr)√(1 - (2πr²/A))      Log On


   

Question 1139171: The surface area of a closed cone of height h and base radius r is given by
A = πr² + πr√(h² + r²).
Show that h = (A/πr)√(1 - (2πr²/A))
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The question is asking to solve for h. Mostly simple algebra.

One of your steps should lead to h=sqrt%28%28%28A-pi%2Ar%5E2%29%2F%28pi%2Ar%29%29%5E2-r%5E2%29,
.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+pi%2Ar%5E2%2B+pi%2Arsqrt%28h%5E2+%2B+r%5E2%29

A+-+pi%2Ar%5E2=pi%2Arsqrt%28h%5E2+%2B+r%5E2%29
A%2F%28pi%2Ar%29+-+%28pi%2Ar%5E2%29%2F%28pi%2Ar%29+=sqrt%28h%5E2+%2B+r%5E2%29

A%2F%28pi%2Ar%29+-+r+=sqrt%28h%5E2+%2B+r%5E2%29...........square both sides

%28A%2F%28pi%2Ar%29+-+r%29%5E2+=h%5E2+%2B+r%5E2

%28A%2F%28pi%2Ar%29%29%5E2+-2%28Ar%2F%28pi%2Ar%29%29%2Br%5E2-r%5E2+=h%5E2+
A%5E2%2F%28pi%5E2%2Ar%5E2%29+-2A%2Fpi++=h%5E2+.......common denominator is %28pi%5E2%2Ar%5E2%29
A%5E2%2F%28pi%5E2%2Ar%5E2%29+-%282A%2Api%2Ar%5E2%29%2F%28pi%5E2%2Ar%5E2%29+=h%5E2+
A%5E2%2F%28pi%5E2%2Ar%5E2%29+-%282A%5E2%2Api%2Ar%5E2%29%2F%28Api%5E2%2Ar%5E2%29+=h%5E2+ factor out common A%5E2%2F%28pi%5E2%2Ar%5E2%29
%28A%5E2%2F%28pi%5E2%2Ar%5E2%29%29%281+-%282pi%2Ar%5E2%29%2FA+%29=h%5E2+

h=sqrt%28%28A%5E2%2F%28pi%5E2%2Ar%5E2%29%29%29%2Asqrt%28%281+-%282pi%2Ar%5E2%29%2FA+%29%29

h=%28A%2F%28pi%2Ar%29%29%2Asqrt%28%281+-%282pi%2Ar%5E2%29%2FA+%29%29