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What is the total surface area of a prism whose volume is 1280 cm3, if cross-section of prism is a square and the ratio of side of square to the height of the prism is 2 ∶ 5?

What is the total surface area of a prism whose volume is 1280 cm3, if cross-section of prism is a square and the ratio of side of square to the height of the prism is 2 ∶ 5? Correct Answer 768 cm<sup>2</sup>

Given, volume of the prism = 1280

Suppose the ratio of side of base to height of prism = 2x ∶ 5x

As we know,

Volume of prism = Area of Base × Height

⇒ 1280 = (2x)2 × 5x

⇒ 20x3 = 1280

⇒ x3 = 1280/20 = 64

⇒ x = ∛64 = 4

Side of the square = 2x = 2 × 4 = 8 cm

Height of the prism = 5x = 5 × 4 = 20 cm

Curved surface area of prism = Perimeter of base × height = 4 × 8 × 20 = 640 cm2

Total surface area of prism = Curved surface area + 2 × Base area = 640 + 2 × 8 × 8 = 640 + 128 = 768 cm2

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