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SSC CGL 2022 PYQ — Question 16

SSC CGL Tier II - Quant - 3 Feb 2022 • Quantitative Aptitude • Q16

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The base of a right pyramid is a square of side 82\sqrt{2} cm and each of its slant edges is of the length of 10 cm. What is the volume (in cm3) of the pyramid?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 256.

Diagonal of a square = 82\sqrt{2} × 2\sqrt{2} = 16

Half of the diagonal of square = 1/2 × 16 = 8 cm.

The slant height( hypotenuse) is 10 cm and the base is 8 cm.

(Height of the pyramid)2 = 102 - 82 = 100 - 64 = 36

h = 6 cm.

Volume of the pyramid = 1/3 × Area of base × height of the pyramid

V = 1/3 ×  82\sqrt{2} ×  82\sqrt{2} × 6 = 256 cm3.