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A right prism of the base equilateral triangle is cut into n equal pieces with a line parallel to base in such a way that base surface area of all the pieces becomes 8 times of the base area of the original prism. If the side of the base of the original prism is 4 cm and volume is 96√3 cm3, then what is the lateral surface area of each piece?

A right prism of the base equilateral triangle is cut into n equal pieces with a line parallel to base in such a way that base surface area of all the pieces becomes 8 times of the base area of the original prism. If the side of the base of the original prism is 4 cm and volume is 96√3 cm3, then what is the lateral surface area of each piece? Correct Answer 36 cm<sup>2</sup>

Since the base surface area of all the pieces becomes 8 times of the base area of the original prism. Hence, the total number of pieces must be equal to 8.

Volume of each small piece = 96√3/8 = 12√3 cm3

Base area × Height = 12√3

(√3/4) × 42 × Height = 12√3

Height = 12√3/4√3 = 3 cm

Lateral surface area of each piece = Perimeter of base × Height

= (3 × 4) × 3

= 36 cm2

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