Question 130

What is the volume (in cm$$^{3}$$) of a right pyramid of height $$12$$ cm and having a square base whose diagonal is $$6\sqrt{2}$$ cm?

Solution

Height of pyramid = $$h=12$$ cm and diagonal of base = $$d=6\sqrt2$$ cm

Let side of square base = $$s$$ cm

=> $$s^2+s^2=d^2$$

=> $$2s^2=(6\sqrt2)^2=72$$

=> $$s^2=\frac{72}{2}=36$$

$$\therefore$$ Volume of pyramid = $$\frac{1}{3}\times$$ Area of base $$\times$$ Height

= $$\frac{1}{3}\times36\times12=144$$ $$cm^3$$

=> Ans - (C)

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