The lateral edge of a regular rectangular pyramid is ' a ' cm long. The lateral edge makes an angle α with the plane of the base. The value of α for which the volume of the pyramid is greatest, is -

Question

The lateral edge of a regular rectangular pyramid is ' a ' cm long. The lateral edge makes an angle α with the plane of the base. The value of α for which the volume of the pyramid is greatest, is - (A) (π/4) (B)  sin -1 √(2/3) (C)  cot -1 √2 (D) (π/3)

Tardigrade Admin · Accepted Answer

Correct answer is (c) cot -1 √2

Q. The lateral edge of a regular rectangular pyramid is ' $a$ ' $c m$ long. The lateral edge makes an angle $α$ with the plane of the base. The value of $α$ for which the volume of the pyramid is greatest, is -

$\frac{π}{4}$

$sin^{- 1} \frac{2}{3}$

$cot^{- 1} 2$

$\frac{π}{3}$

Correct answer is (c) $cot^{- 1} 2$

Q. The lateral edge of a regular rectangular pyramid is ' a ' cm long. The lateral edge makes an angle α with the plane of the base. The value of α for which the volume of the pyramid is greatest, is -

4π​

sin−132​​

cot−12​

3π​