The wading pool shown is a trapezoidal prism with a height of a total volume of 286 cubic feet. What is the missing dimension?
**The drawing shows the shallow height is 2ft. Length is 13ft. Width is 8ft. And a question mark for the height of the deeper end of pool.
THANK YOU!!
3.5 ft
Make a sketch showing the trapezoid in a side view.
Volume = (area of trap) x 8
= (13(2 + h)/2)(8)
= 52(2+h) = 286
104 + 52h = 286
h = .....
To find the missing dimension, which is the height of the deeper end of the pool, we can use the formula for the volume of a trapezoidal prism:
Volume = ((base1 + base2) / 2) * height * length
In this case, we know the total volume is 286 cubic feet, the shallow height is 2ft, the length is 13ft, and the width is 8ft. Let's plug in these values into the formula:
286 = ((base1 + base2) / 2) * 2 * 13
First, let's calculate the sum of the bases:
286 = ((base1 + base2) / 2) * 26
Next, let's simplify the equation by multiplying both sides by 2:
572 = (base1 + base2) * 26
Now, let's find the sum of the bases:
572 = 26 * (base1 + base2)
To isolate the sum of the bases, divide both sides by 26:
22 = base1 + base2
Since the drawing shows a trapezoidal pool, we know that base1 is the width of the shallow end and base2 is the width of the deeper end. We already know that the width is 8ft. So, let's substitute this value into the equation:
22 = 8 + base2
Subtracting 8 from both sides of the equation:
14 = base2
Therefore, the missing dimension, which is the height of the deeper end of the pool, is 14ft.