The slant height of a square pyramid is 10 cm and its surface area is 144 square centimetres. What is the volume of the square pyramid?

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Solution

Note first that the Volume of a square pyramid = $\frac{1}{3} \times B a s e a r e a \times H e i g h t$
Given that the base area of the square pyramid = 144cm and the slant height of a square pyramid is 10 cm
$⟹ B a s e e d g e = \sqrt{144} = 12 c m$
Now, $H e i g h t o f t h e s q u a r e p y r a m i d = \sqrt{(S l a n t h e i g h t o f t h e p y r a m i d)^{2} - (H a l f t h e b a s e e d g e)^{2}} = \sqrt{100^{2} - 6^{2}} = \sqrt{100 - 36} = \sqrt{64} = 8 c m$
Thus, the required volume = $\frac{1}{3} \times 144 \times 8 = 384 c u b i c c e n t i m e t r e s$

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