Question

If the volume of the tetrahedron formed by the coterminous edges `bar"a", bar"b" and bar"c"` is 5, then the volume of the parallelopiped formed by the coterminous edges `bar"a" xx bar"b", bar"b" xx bar"c" and bar"c" xx bar"a"` is

Options

• 400

• 576

• 900

• 1296

Answer 1

900

Explanation:

Volume of tetrahedron = `1/6 [bar"a"  bar"b"  bar"c"]`

`=> 5 = 1/6 [bar"a"  bar"b"  bar"c"] => [bar"a"  bar"b"  bar"c"] = 30`

Edges of parallelopiped are `bar"a" xx bar"b", bar"b" xx bar"c", bar"c" xx bar"a"`

∴ Volume of parallelopiped = `[bar"a" xx bar"b"   bar"b" xx bar"c"  bar"c" xx bar"a"]`

`= [bar"a"  bar"b"  bar"c"]^2`

= 30²

= 900 sq. units