Multiple choice

A square pyramid with side 10 cm has a volume of 400 cm3. Find the total surface area of the pyramid.

  1. $360 cm2$
  2. $529 cm2$
  3. $421 cm2$
  4. $530 cm2$
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A Correct answer
Explanation

Square pyramid with side a = 10 cm, volume V = 400 cm³. Volume formula: V = (1/3) × base_area × height = (1/3) × 100 × h = 400, so h = 12 cm. Slant height l = sqrt((a/2)² + h²) = sqrt(25 + 144) = 13 cm. Surface area = base_area + 4 × (1/2 × a × l) = 100 + 2 × 10 × 13 = 100 + 260 = 360 cm². Find height from volume first, then calculate slant height for surface area.

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