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Question

If $v_{1}, v_{2}, v_{3}$ are the volumes of parallelopiped triangular prism and tetrahedron respectively and three coterminous edges of all figures are $\to a, \to b, \to c$ then $v_{1}, v_{2}, v_{3}$ equals

A

1 : 3 : 6

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B

6 : 1 : 3

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C

6 : 3 : 1

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D

None of these

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Solution

The correct option is C $6 : 3 : 1$
As $\to a, \to b, \to c$ are coterminums edges of all figures
$∴ v_{1} = [\to a \to b \to c], v_{2} = \frac{1}{2} [\to a \to b \to c], v_{3} = \frac{1}{6} [\to a \to b \to c]$
$∴ v_{1} : v_{2} : v_{3} = 1 : \frac{1}{2} : \frac{1}{3} = 6 : 3 : 1$

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