Question

Find the value of a in terms of A for the given equation

A=3πa², for a
A. a=(±√(Aπ))/3
B. a=(±√(3πA))/(3π)
C. a=√(3πA)
D. a=(±A√(3π))/(3π)

Answer 1

The value of 'a' in terms of 'A' for the equation A=3πa² is found by dividing both sides by 3π and then taking the square root. The correct expression is a = ( ±√(Aπ) ) / 3, which matches option A.

Step-by-step explanation:

The student is asking to find the value of a in terms of A for the given equation A=3πa². To do this, we need to solve the equation for a. We begin by dividing both sides of the equation by 3π:

A / 3π = a².

Next, we take the square root of both sides to solve for a:

a = ±√(A / 3π).

To simplify the expression, we place the square root over each factor in the denominator:

a = ±√(A) / √(3π).

Since we are seeking a in terms of A, the correct answer should match this form. Among the given options, the one that matches is:

a = ( ±√(Aπ) ) / 3, which corresponds to option A. This is the correct expression for a in terms of A for the equation A=3πa².