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In the figure above, the bases , ABC and...

In the figure above, the bases , ABC and DEF, of the right prism are equilateral triangles. The altitude of the prism is BE. If a plane cuts the figure through points A, C and E, two solids, EABC, and EACFD, are formed. What is the ratio of the volume of EABC to the volume of EACFD?

A

`1/4`

B

`1/3`

C

`(sqrt3)/(4`

D

`1/2`

Text Solution

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The correct Answer is:
D
The volume of the prism is area of base times height. The figure EABC is a pyramid with base triangle ABC and height BE, the same as the base the height of the prism. The volume of the pyramid is `1/3`(base times height),`1/3` the volume of the prism. Therefore, the other solid EACFD, is `2/3` the volume of the prism. The ratio of the volume is `1/2`. [15]
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