To solve the problem we will calculate the volume of both the prism separately and then we will add both the volumes.
Volume of Prism
The volume of any prism is given as the product of its base area and the height of the prism.
[tex]\rm{Volume\ of\ Prism =(Base\ Area)\times height[/tex]
The volume of Jane's ramp is 11.5 m³.
Given to us,
- AB = 3.5 m
- BC = 4 m
- CD = 1 m
- AH = 2 m,
Solution
Volume of triangular Prism
[tex]\rm{Volume\ of\ Prism =(Base\ Area)\times height[/tex]
for the triangular prism, the base area will be ΔABG
[tex]\begin{aligned}Area \triangle &= \dfrac{1}{2} \times AB \times AH\\
&=\dfrac{1}{2}\times 3.5 \times 1\\
& = 1.75 \ m^2\end{aligned}[/tex]
The volume of the triangular Prism = Base area x height
= Area ΔABG x 2 m
= 1.75 m² x 2 m
= 3.5 m³
Volume of the rectangular Prism
[tex]\rm{Volume\ of\ Prism =(Base\ Area)\times height[/tex]
for the rectangular prism, the base area will be BCDG
[tex]\begin{aligned}Area\ BCDG &= BC \times CD\\
& = 4 \times 1\\
&= 4\ m^2\end{aligned}[/tex]
The volume of the rectangular Prism = Base area x height
= Area BCDG x 2 m
= 4 m² x 2 m
= 8 m³
Total volume of the ramp
Total volume of the ramp
= Volume of triangular Prism + Volume of rectangular Prism
= 3.5 m³ + 8 m³
= 11.5 m³
Hence, the volume of Jane's ramp is 11.5 m³.
Learn more about Prism:
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