Question
A layer of crushed rock must be spread Over a circular area 23 feet in diameter how deep a layer will be obtained using 200 ft^3 of rock
The depth of the layer is blank feet
The depth of the layer is blank feet
Answers
GPT 3.5
To find the depth of the layer, we first need to calculate the area of the circular area.
Area of a circle = πr^2
Given that the diameter is 23 feet, the radius (r) is half of the diameter, so r = 23/2 = 11.5 feet
Area = π(11.5)^2 = 415.08 ft^2
Now, we need to find the volume of the layer by multiplying the area by the depth.
Volume = Area x Depth
Given that 200 ft^3 of rock is spread over the circular area, we can set up the equation as:
200 = 415.08 x Depth
Solving for Depth:
Depth = 200 / 415.08
Depth ≈ 0.482 feet
Therefore, a layer of crushed rock with a depth of approximately 0.482 feet will be obtained using 200 ft^3 of rock over a circular area with a diameter of 23 feet.
Area of a circle = πr^2
Given that the diameter is 23 feet, the radius (r) is half of the diameter, so r = 23/2 = 11.5 feet
Area = π(11.5)^2 = 415.08 ft^2
Now, we need to find the volume of the layer by multiplying the area by the depth.
Volume = Area x Depth
Given that 200 ft^3 of rock is spread over the circular area, we can set up the equation as:
200 = 415.08 x Depth
Solving for Depth:
Depth = 200 / 415.08
Depth ≈ 0.482 feet
Therefore, a layer of crushed rock with a depth of approximately 0.482 feet will be obtained using 200 ft^3 of rock over a circular area with a diameter of 23 feet.