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If the height of the square base pyramid is equal to the side of the Tetrahedron whose height is 4√6 cm and the side of the square base pyramid is 7 cm. What will be the volume of the square base pyramid?

If the height of the square base pyramid is equal to the side of the Tetrahedron whose height is 4√6 cm and the side of the square base pyramid is 7 cm. What will be the volume of the square base pyramid? Correct Answer 196 cm<sup style="">3</sup>

Given:

Height of the tetrahedron = 4√6 cm

Side of the square base pyramid(S) = 7 cm 

Formula used:

Height of the tetrahedron = √2a/√3

Volume of the square base pyramid = 1(/3) × (side)2 × Height of the pyramid

Calculations:

Height of the tetrahedron = √2a/√3

4√6 = √2a/√3

a = (4√6 × √3)/√2 

a = 12√2/√2 

a = 12 cm

Height of the square base pyramid = side of the tetrahedron = 12 cm

Volume of the square base pyramid = 1(/3) × (side)2 × Height of the pyramid

Volume of the square base pyramid = 1(/3) × (7)2 × 12

Volume of the square base pyramid = 49 × 4

∴ Volume of the square base pyramid = 196 cm3

Alternate Method:

Solve by substituting the options.

 The Side of the square pyramid is 7 cm which means it will be in the answer so we check the option for 72 multiples.

We see that option 2 contains the 72 multiples. Hence, we can say that option 2 is the answer.

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