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    Question

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

    and vertical height 12 cm. Find: (i) its volume, (ii) its slant height, (iii) its lateral surface area.
    A Volume = 400 cm³ ; slant height = 33 cm and lateral surface area = 260 cm² Correct Answer Incorrect Answer
    B Volume = 400 cm³ ; slant height = 13 cm and lateral surface area = 260 cm² Correct Answer Incorrect Answer
    C Volume = 100 cm³ ; slant height = 13 cm and lateral surface area = 260 cm² Correct Answer Incorrect Answer
    D Volume = 400 cm³ ; slant height = 13 cm and lateral surface area = 160 cm² Correct Answer Incorrect Answer

    Solution

    (i) Volume of a pyramid = (1/3) × (area of base) × height Base area = 10 × 10 = 100 cm² Volume = (1/3) × 100 × 12 = 400 cm³ (ii) Slant height l is the height of a triangular face. In right square pyramid, l is the hypotenuse of right triangle with one leg = vertical height h = 12, other leg = half the base side = 5. l = √(h² + (side/2)²) = √(12² + 5²) = √(144 + 25) = √169 = 13 cm (iii) Lateral surface area = sum of areas of 4 congruent triangular faces. Area of one triangle = (1/2) × base × slant height = (1/2) × 10 × 13 = 65 cm² Lateral surface area = 4 × 65 = 260 cm²

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