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      Question

      A right square pyramid has a base of side 10 cm and

      slant height 13 cm. (a) Find its lateral surface area. (b) If its vertical height is 12 cm, find its volume.
      A 260 cm² and 400 cm³ Correct Answer Incorrect Answer
      B 264 cm² and 470 cm³ Correct Answer Incorrect Answer
      C 260 cm² and 500 cm³ Correct Answer Incorrect Answer
      D 164 cm² and 490 cm³ Correct Answer Incorrect Answer

      Solution

      (a) Area of one triangular face = (1/2) × base × slant height = (1/2) × 10 × 13 = 65 cm² There are 4 faces: Lateral surface area = 4 × 65 = 260 cm² (b) Volume = (1/3) × (area of base) × height Base area = 10 × 10 = 100 cm² Volume = (1/3) × 100 × 12 = 400 cm³.

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