The surface area of a cylinder with height h and a circular top with radius r is given by the formula:
A = 2πr^2 + 2πrh
We know the surface area, so we can use this formula to find the radius of the circular top:
354 = 2πr^2 + 2πrh
354 = 2πr^2 + 40πr
354 = 2πr^2 + 40πr
354 = 2πr(r + 20)
We can now solve for r:
354 = 2πr(r + 20)
177 = πr(r + 20)
177 = πr^2 + 20πr
177 = πr^2 + 20πr
πr^2 + 20πr - 177 = 0
We can use the quadratic formula to find the value of r:
r = (-b ± √(b^2 - 4ac)) / 2a
Where a = π, b = 20π, c = -177
r = (-20π ± √(20^2 - 4(π)(-177))) / (2 * π)
r = (-20π ± √(400π^2 + 708)) / (2 * π)
r = (-20π ± √(708 + 400π^2)) / (2 * π)
r = (-20π ± √(708 + 400 * π^2)) / (2 * π)
Since the radius must be positive, we'll use the positive square root:
r = (-20π + √(708 + 400 * π^2)) / (2 * π)
Using the value of π = 3.14, we can calculate the value of r to be approximately 6.93 cm. Rounding to the nearest hundredth, we get:
r = 6.93 cm (rounded to the nearest hundredth)