Question : The base of a right pyramid is an equilateral triangle with a side of 8 cm, and its height is $30 \sqrt{3}$ cm. The volume (in cm$^3$ ) of the pyramid is:
Option 1: $240 \sqrt{3}$
Option 2: $360 \sqrt{3}$
Option 3: $480$
Option 4: $360$
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Correct Answer: $480$
Solution :
Volume of pyramid = $\frac{1}{3}$ × area of base × height
= $\frac{1}{3}$ × area of equilateral triangle × height
= $\frac{1}{3}×\frac{\sqrt3}{4}$ × (8)
2
× $30 \sqrt{3}$
= $\frac{\sqrt3}{4}$ ×64
= 480 cm
3
Hence, the correct answer is $480$.
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