Question 57

Base of a right pyramid is a square, length of diagonal of the base is 24$$\sqrt{2}$$ m. If the volume of the pyramid is 1728 cu.m. its height is

Solution

$$ area of the base = \frac{1}{2} \times (diagonal)^2 $$

= $$ \frac{1}{2} \times 24 \sqrt{2} \times 24 \sqrt{2} = 576 cm^2 $$

volume of the pyramid = $$ \frac{1}{3} \times area of base \times height $$

$$ 1728 = \frac{1}{3} \times h \times 576 $$

$$ h = \frac{1728 \times 3}{576} = 9 m $$

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