Use the formula for the surface area of a right cone, A=πr(r+√h^2+r^2), to answer the question.
show how this formula can be rearranged to solve for h
correcting your formula:
A=πr(r+√(h^2+r^2))
A = πr^2 + √(h^2+r^2)
A - πr^2 = √(h^2+r^2)
square both sides
(A - πr^2) = h^2 + r^2
(A - πr^2) - r^2 = h^2
h = √[ (A - πr^2) - r^2 ]
To rearrange the formula for the surface area of a right cone, A = πr(r + √(h² + r²)), to solve for h, we can follow these steps:
Step 1: Start with the given formula: A = πr(r + √(h² + r²)).
Step 2: Expand the expression inside the square root: A = πr(r + √(h² + r²)) = πr² + πr√(h² + r²).
Step 3: Isolate the term containing the square root on one side of the equation: A - πr² = πr√(h² + r²).
Step 4: Square both sides of the equation to eliminate the square root: (A - πr²)² = (πr√(h² + r²))².
Step 5: Simplify the equation: (A - πr²)² = π²r²(h² + r²).
Step 6: Expand the equation: A² - 2Aπr² + (πr²)² = π²r²h² + π²r⁴.
Step 7: Rearrange the equation by moving all terms involving h to one side: π²r²h² = A² - 2Aπr² + (πr²)² - π²r⁴.
Step 8: Divide both sides of the equation by π²r² to solve for h²: h² = (A² - 2Aπr² + (πr²)² - π²r⁴) / (π²r²).
Step 9: Take the square root of both sides to find h: h = √[(A² - 2Aπr² + (πr²)² - π²r⁴) / (π²r²)].
Therefore, by rearranging the formula, we have found an expression that can be used to solve for h in terms of A and r.