tmua.me Extreme Set A Paper 1 · Question 19

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tmua.me Extreme Set A Paper 1 · Q19

Paper 1Geometry

A cube has side length $1$ . Two distinct parallel planes, $\Pi_1$ and $\Pi_2$ , are each perpendicular to the same body diagonal $VW$ .

Each plane cuts the cube in a polygon of area $\dfrac{11\sqrt3}{16}$ .

What is the perpendicular distance between the two planes?

\dfrac{\sqrt3}{12}

\dfrac16

\dfrac14

\dfrac{\sqrt3}{6}

\dfrac{\sqrt3}{4}

\dfrac12

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