Answer:
Part (a)
2.4m × 0.4m × 0.6m
2.4m × 0.4m × 1.2m
2.4m × 0.4m × 1.8m
Part (b)
3.456 m³
Step-by-step explanation:
If each stair is the same length, width and height then:
- length of stair = 2.4 m
- height of stair = 1.8 ÷ 3 = 0.6 m
- width (depth) of stair = 1.2 ÷ 3 = 0.4 m
Part (a)
The set of stairs can be broken into 3 rectangular prisms.
Divide the stairs by drawing vertical lines from the vertices (see attachment for annotated diagram). Therefore each rectangular prism has the same length and width, but a different height.
Volume of a rectangular prism = L × W × H
Therefore, the dimensions of each solid figure (L × W × H) are:
- Red: 2.4m × 0.4m × 0.6m
- Yellow: 2.4m × 0.4m × 1.2m
- Green: 2.4m × 0.4m × 1.8m
Part (b)
To calculate the volume of concrete needed to form the stairs, sum the volumes of the rectangular prisms:
[tex]\begin{aligned}\implies \textsf{Volume of concrete} & = \sf (2.4 \times 0.4 \times 0.6) + (2.4 \times 0.4 \times 1.2) + (2.4 \times 0.4 \times 1.8)\\& = \sf 0.576 + 1.152 + 1.728\\&= \sf 3.456\:\:m^3\end{aligned}[/tex]
