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The base of a right prism, whose height is 2 cm, is a square. If the total surface area of the prism is 10 cm², then its volume is :
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- 3 cm³
- 1 cm³
- 2 cm³
- 4 cm³
- 3 cm³
Correct Option: C
Total surface area of prism = Perimeter of base × height + 2 × area of base
10 = 4x × 2 + 2x²
where x = side of square
⇒ x² + 4x – 5 = 0
⇒ x² + 5x – x – 5 = 0
⇒ x (x + 5) –1 (x + 5) = 0
⇒ (x – 1) (x + 5) = 0
⇒ x = 1 because x ≠ –5
∴ Volume of prism = Area of base × height = 1 × 1 × 2 = 2 cu.cm.
