Question

the area of a circle is 36π cm². what is the radius of this circle?

Answer 1

Since we know that area A = 36π, we can substitute into the formula for area A and get:

36π= πr²

Now, dividing both sides by π in order to begin isolating r on one side of the equation, we get:

(36π)/π = (πr²)/π

36(π/π) = (π/π)r²

36(1) = (1)r²

36 = r²

r² = 36 (since equality is symmetric, i.e., if a = b, than b =a)

Now, taking the square root of both sides, we have:

√(r²) = ±√(36)

r = √(36) (since a distance cannot be physically negative, then we have to use the positive square root)

r = 6 (since (6)(6) = 36)

CHECK:

A = 36π

36π= π(6²)

36π = π(36)

36π = 36π

Therefore, r = 6 is indeed the radius of the circle with an area of 36π

Answer 2

Answer:

$area \: of \: circle \: = \pi {r}^{2} \: 36\pi \: \: = \pi {r}^{2} \: {r}^{2} = 36 \: \: \: r = 6cm$