Final answer:
The depth of the layer is 0.58 ft.
Step-by-step explanation:
To calculate the depth of a layer of crushed rock spread over a circular area with a diameter of 21 feet using 200 ft³ of rock, we must first find the area of the circle. Since the area (A) of a circle is calculated with the formula A = πr², where r is the radius of the circle and π (pi) is approximately 3.14159, we can find the area of the circle by taking half of the diameter as the radius, which in this case would be 10.5 feet.
Therefore, the area of the circle is π * (10.5 ft)² = π * (110.25 ft²) = 346.36059 ft² (rounded to five decimals).
Next, to find the depth of the rock layer, we divide the volume of rock by the area of the circle: depth = volume / area = 200 ft³ / 346.36059 ft². This calculation results in a depth of approximately 0.577 ft, which is around 6.93 inches when converted to inches (1 foot = 12 inches).
Therefore, a 200 ft³ volume of crushed rock will create approximately a 0.577-foot-deep layer over a circular area 21 feet in diameter. If we round this to the nearest hundredth, as the question asks, we get a layer depth of 0.58 feet.