QA) Which solid figures can the staircase be broken into?
A) The staircase can be broken into 3 rectangular prisms.
QB) What are the dimensions of each solid figure?
A) We are given the height (2.5 ft) and the length (3 ft) of the entire staircase. To find the height and length of each step, just divide by 3:
2.5 / 3 = 5/6 ft high
3 / 3 = 1 ft long
Looking at the image given, we can see that the staircase is 6 ft wide.
Bottom prism: 3 ft long, 6 ft wide, and 5/6 ft high.
Middle prism: 2 ft long, 6 ft wide, and 5/6 ft high.
Top prism: 1 ft long, 6 ft wide, and 5/6 ft high.
QC) How much concrete will be needed to form the staircase?
A) To answer this question, we have to find the volume of each rectangular prism. The formula for the volume of a rectangular prism is
V = lwh; where l = length, w = width, and h = height.
We need to apply this formula to each prism. I'll go from the bottom up.
(1.) V = lwh; l = 3, w = 6, h = 5/6
V = (3)(6)(5/6)
V = 15 ft²
(2.) V = lwh; l = 2, w = 6, h = 5/6
V = (2)(6)(5/6)
V = 10 ft²
(3.) V = lwh; l = 1, w = 6, h = 5/6
V = (1)(6)(5/6)
V = 5 ft²
To find the amount of concrete needed to form the staircase, just add the volumes of the three rectangular prisms:
15 + 10 + 5 = 30 ft²
The contractor will need enough concrete to cover 30 ft² to form the staircase.
Hope this helps!