Discussion

Explanation:

The vertical edge makes an angle of 60° with the side of the base, Let us consider the vertical triangle OAB.

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In triangle OAB, the two base angles are 60°, hence the vertical angle will also be 60°.
∴ OAB is an equilateral triangle,
⇒ The slant height of the pyramid = height of triangle OAB = √3/2 × 4 = 2√3

Now, in right triangle OPQ,

OP = height of the pyramid,
PQ = 4/2 = 2
​​​​​​​OQ = 2√3.

∴ OQ² = PO² + PQ²
⇒ 12 = h² + 4
⇒ h² = 8
⇒ h = 2√2

Now, Volume of pyramid = 1/3 × (base area) × (height) = 1/3 × 16 × 2√2 = 32√2/3.

Hence, option (a).

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