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 <em>A</em>.
Also given that Height of prism = Height of cylinder = <em>6</em>
Volume of a prism is given as:
![V_{Prism} = \text{Area of cross section} \times Height](https://tex.z-dn.net/?f=V_%7BPrism%7D%20%3D%20%5Ctext%7BArea%20of%20cross%20section%7D%20%5Ctimes%20Height)
![V_{Prism} = A \times 6 ........ (1)](https://tex.z-dn.net/?f=V_%7BPrism%7D%20%3D%20A%20%5Ctimes%206%20........%20%281%29)
Cross section of cylinder is a circle.
<em>Area of circle</em> is given as: ![\pi r^{2}](https://tex.z-dn.net/?f=%5Cpi%20r%5E%7B2%7D)
Area of cross section, A = ![\pi r^{2}](https://tex.z-dn.net/?f=%5Cpi%20r%5E%7B2%7D)
Volume of cylinder is given as:
![V_{Cylinder} = \pi r^{2} h\\\Rightarrow V_{Cylinder} = A \times h\\\Rightarrow V_{Cylinder} = A \times 6 ...... (2)](https://tex.z-dn.net/?f=V_%7BCylinder%7D%20%3D%20%5Cpi%20r%5E%7B2%7D%20h%5C%5C%5CRightarrow%20V_%7BCylinder%7D%20%3D%20A%20%5Ctimes%20h%5C%5C%5CRightarrow%20V_%7BCylinder%7D%20%3D%20A%20%5Ctimes%206%20......%20%282%29)
From equations (1) and (2) we can see that
![V_{Prism}=V_{Cylinder}](https://tex.z-dn.net/?f=V_%7BPrism%7D%3DV_%7BCylinder%7D)
Hence, the correct answer is:
Volume of prism is equal to the volume of cylinder.