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The slant height of a square pyramid is 25 centimetres and its surface area is 896 square centimetres. What is its volume? |
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Answer» l = 25 cm Surface area = 896 cm a2 + 2al = 896 a2 + 2a × 25 = 896 a2 + 50a – 896 = 0 a = \(\frac{50\pm\sqrt{2500+3584}}{2}\) = \(\frac{50\pm\sqrt{6084}}{2}\) = \(\frac{50\pm78}{2}\) a = \(\frac{50+78}{2}\) or \(\frac{50-78}{2}\) = \(\frac{28}{2}=14\) or \(\frac{-128}{2}=-64\) Length of base edge = 14 cm height h = \(\sqrt{1^2-(\frac{a}{2})^2}\) = \(\sqrt{25^2-7^2}\) = \(\sqrt{625-49}\) = \(\sqrt{576}\) = 24 Volume = \(\frac{1}{3}a^2h\) = \(\frac{1}{3}\) x 142 x 24 = 1568 cm3 |
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