A Circular pool has radius 5.9m. You want to build a cement walkway around it and you have 23 sq m of cement

How wide can you make your walkway? Possible answers: A) 54cm B) 59cm C) 64cm D) 69cm E)74cm

Suppose that the width of the walkway is w. The area of the walkway is the between the area of the surface of the pool and the area enclosed by the both the pool and the walkaway.

The area of the pool's surface is π(5.9)^2 and the area of the surface of the pool plus the walkway is π(5.9 + w)^2. The area of the walkway is then:
π(5.9 + w)^2 - π(5.9)^2.

We only have 23 m^2 of walkway, so:
π(5.9 + w)^2 - π(5.9)^2 = π[(5.9 + w)^2 - 5.9^2] = 23.

Solving this equation:
π[(5.9 + w)^2 - 5.9^2] = 23
==> (5.9 + w)^2 - 5.9^2 = 23/π
==> (5.9 + w)^2 = 23/π + 5.9^2
==> 5.9 + w = √(23/π + 5.9^2), by taking the positive square root of both sides
==> w = √(23/π + 5.9^2) - 5.9 ≈ 0.59 m = 59 cm.

Therefore, the answer is (B).

I hope this helps!

area of pool and walkway = area of pool + area of walkway...equation 1
area of pool and walkway = (pool radius + walkway width)^2 pi...equation 2
For equation 1, area of pool and walkway = 5.9^2 pi + 23 = 132.3
Substitute 131.3 into equation 2, letting x = walkway width:
132.3 = (5.9 + x)^2 pi
42.13 = (5.9 + x)^2
5.9 + x = 6.49 or 5.9 + x = -6.49
x = 0.59 or x = -12.39
A negative width makes no sense so discard x = -12.39, leaving just
x = 0.59m = 59cm
Answer is B.

B) 59cm