Question

The height, width and length of the steps are identical. Calculate the cubic feet of concrete needed to create the stairwell.

A) 81 cubic feet
B) 135 cubic feet
C) 162 cubic feet
D) 270 cubic feet

Answer 1

The answer is C) 162!

Count the number of rectangular prisms needed to make the stairwell (6) and multiply it by the volume of each prism (1.5x3x6). 6 x 27 = 162 cubic feet

Answer 2

The correct answer is c) 162
`ft^(3)`

Explanation:

We know that the height, width and length of the steps are identical. We also have the measures of a step. In order to calculate the cubic feet of concrete needed to create the stairwell we will need to calculate the volume of the stairwell.

The volume of one step is :

`V_(step)=(6ft).(1.5ft).(3ft)=27ft^(3)`

Finally, we can imaginary subdivide the stairwell into 6 steps.

First we have a step. Then, we have two steps (one over each other). Finally, we have three steps (one over each other).

To calculate the volume of the stairwell, we can perfom the following calculation :

`V_(stairwell)=6.(V_(step))`

`V_(stairwell)=(6).(27ft^(3))=162ft^(3)`

We found out that the volume of concrete needed to create the stairwell is
`162ft^(3)`