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The height of a right prism with a square base is 15 cm. If the area of the total surface of the prism is 608 sq. cm, its volume is
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- 910 cm³
- 920 cm³
- 960 cm³
- 980 cm³
- 910 cm³
Correct Option: C
Total surface area of prism = Curved surface area + 2 × Area of base
⇒ 608 = perimeter of base × height + 2 × Area of base
⇒ 608 = 4x × 15 + 2x² (Where x = side of square)
⇒ x² + 30x – 304 = 0
⇒ x² + 38x – 8x – 304 = 0
⇒ x (x + 38) – 8 (x + 38) = 0
⇒ (x – 8) (x + 38) = 0
⇒ x = 8
⇒ Volume of prism = Area of base × height = 8 × 8 × 15 = 960 cu.cm.
