Answer:
The correct answer is:
The volume of the triangular prism is equal to the volume of the cylinder
Step-by-step explanation:
Given that there are two figures
1. A right triangular prism and
2. Right cylinder
Area of cross section of prism is equal to Area of cross section of cylinder.
Let this value be A.
Also given that Height of prism = Height of cylinder = 6
Volume of a prism is given as:
[tex]V_{Prism} = \text{Area of cross section} \times Height[/tex]
[tex]V_{Prism} = A \times 6 ........ (1)[/tex]
Cross section of cylinder is a circle.
Area of circle is given as: [tex]\pi r^{2}[/tex]
Area of cross section, A = [tex]\pi r^{2}[/tex]
Volume of cylinder is given as:
[tex]V_{Cylinder} = \pi r^{2} h\\\Rightarrow V_{Cylinder} = A \times h\\\Rightarrow V_{Cylinder} = A \times 6 ...... (2)[/tex]
From equations (1) and (2) we can see that
[tex]V_{Prism}=V_{Cylinder}[/tex]
Hence, the correct answer is:
Volume of prism is equal to the volume of cylinder.
