solve for a: V=4/3pia^2b
V = (4/3) pi a^2 b
This looks like an equation for the volume of an prolate spheroid. (They have the shape of a rugby ball). To solve for a, divide both sides of the equation by (4/3) pi b and then take the positive square root of both sides.
To solve for 'a' in the equation V = (4/3)πa^2b, where V is the volume, π is pi (approximately 3.14159), and b is a constant, you can follow these steps:
Step 1: Start with the equation V = (4/3)πa^2b.
Step 2: Divide both sides of the equation by (4/3)πb to isolate a^2.
V / ((4/3)πb) = a^2
Step 3: Simplify the right side of the equation by dividing.
(3V) / (4πb) = a^2
Step 4: Take the square root of both sides to find 'a'.
√[(3V) / (4πb)] = a
So, the solution for 'a' is √[(3V) / (4πb)].
To solve for 'a' in the equation V = (4/3)πa^2b, we need to isolate the variable 'a'.
First, let's rewrite the equation in a simplified form:
V = (4π/3)a^2b
To isolate 'a', we need to get rid of the constant terms and other variables on the same side as 'a'. Here's how we can do it step by step:
1. Divide both sides of the equation by (4π/3):
V / (4π/3) = a^2b
2. Multiply both sides by the reciprocal of b:
(V / (4π/3)) * (1/b) = a^2
(3V) / (4πb) = a^2
3. Take the square root of both sides:
√((3V) / (4πb)) = √(a^2)
√((3V) / (4πb)) = a
Thus, the value of 'a' is √((3V) / (4πb)).
Note: Keep in mind that the square root can have both positive and negative solutions. If you're dealing with physical quantities, you should choose the positive value of 'a' as the dimension of length can only be positive.