Question

A contractor is building a set of stairs out of concrete. Each stair is exactly the same length, width, and height.

Staircase
Diagram shows a set of three steps of a staircase. Height of the third step from the ground measures 1.8 meters. The width from the front of the staircase to the back of the staircase measures 1.2 meters. The length of the steps measures 2.4 meters.

Which solid figures can the stairs be broken into? What are the dimensions of each solid figure?

How much concrete will be needed to form the stairs?

Answer 1

top rectangular prism = .6 x .4 x 2.4

middle rectangular prism = .6 x .8 x 2.4

bottom rectangular prism = .6 x 1.2 x 2.4

concrete needed = 3.672 cubic meters

Explanation:

The steps can be broken into bottom step from front to back, middle step from front to back, top step from front to back resulting in

three rectangles

The dimensions of each solid figure can be found since we know the steps are equal so we divide the height and width by 3 equal parts and the length stays the same. So...

1.8/3=.6 m

1.2/3=.4 m

top rectangular prism = .6 x .4 x 2.4

middle rectangular prism = .6 x .8 x 2.4

bottom rectangular prism = .6 x 1.2 x 2.4

Find the volume by plugging our dimensions into the formula for volume for each step and then add all three steps together for total volume...

.6 x .4 x 2.4= .576

.6 x .8 x 2.4= 1.152

.6 x 1.2 x 2.4=1.944

add totals together...

.576 + 1.152 + 1.944=3.672

Answer 2

Dimensions:

H = 0.9 m

W = 0.4 M

L = 2.4 m

Explanation:

As they are all the same dimensions and there are only 3 stairs, divide all the figures (except the length as it will stay the same) by 3 to get your figures.