SOLUTION: David and Sandra Jessee are planning to build a ramp so that the front entrance of their home will be wheelchair accessible. The ramp will be 3-feet wide. It will rise 2in. for ea

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Question 1034667: David and Sandra Jessee are planning to build a ramp so that the front entrance of their home will be wheelchair accessible. The ramp will be 3-feet wide. It will rise 2in. for each foot of length of horizontal distance. Where the ramp meets the porch, the ramp must be 2ft high. To prove stability for the ramp, the Jessees will install a slab of concrete 4in thick and 6in longer and wider tha the ramp. The top of the slab will be level with the ground. The ramp may be constructed of a concrete or pressure-treated lumber. You are to estimate the cost of materials for constructing the slab, the ramp of concrete, and the ramp of pressure-treated lumber.
a) Determine the length of the base of the ramp.
b) Determine the dimensions of the concrete slab on which the will set.
c) Determine the volume of the concrete in cubic yards needed to construct the slab.
d) if ready mix concrete cost $45 per cubic yard, determine the cost of the concrete needed to construct the slab.
Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website!
Rise:
2ft = 24 inches high, rising 1 ft every 2 inches
Run:
24/2 = 12 feet is the length of the base of the ramp.
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2^2+12^2 = 148; √148 = 12.166 is the length of the incline (the ramp)
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Dimensions of the concrete slab: see picture below
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Volume of concrete:
Area of the side of the ramp: (12*2)/2 = 12
Volume:
1/2*2*12*3 = 36 cubic feet. Convert it to yards to get your answer.