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What is the surface area of a square pyramid of base perimeter 64 centimetres and volume 1280 cubic centimetres? |
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Answer» Base perimeter 4a = 64 a = 16 cm Volume = \(\frac{1}{3}a^2h=1280\) a2h = 1280 x 3 h = \(\frac{1280\times3}{a^2}\) = \(\frac{1280\times3}{16^2}\) = \(\frac{3840}{256}\) = 15 cm \(l=\sqrt{h^2+(\frac{a}{2})^2}\) = \(\sqrt{15^2+8^2}\) = \(\sqrt{289}\) = 17 Surface area = a2 + 2al = 162 + 2 × 16 × 17 = 256 + 544 = 800 cm2 |
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