Question

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

(a) Which solid figures can the stairs be broken into? What are the dimensions of each solid figure?
(b) How much concrete will be needed to form the stairs?
Answer:

Answer 1

(A) The stairs can be broken down into 3 cylinders.
Dimensions of the first cylinder formed = 2.4m by 0.4m by 0.6m.
Dimensions of the second cylinder formed = 2.4m by 0.4m by 1.2m
Dimensions of the third cylinder formed = 2.4m by 0.4m by 1.8m

(B) Volume of the first cylinder = 2.4m×0.4m×0.6m = 0.576m^3
Volume of the second cylinder = 2.4m×0.4m×1.2m = 1.152m^3
Volume of the third cylinder = 2.4m×0.4m×1.8m = 1.728m^3

Therefore, volume of the whole stairs = (0.576+1.152.1.728)m^3 =3.456m^3

Hence, 3.456m^3 of concrete will be needed to form the stairs.

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