Question : A right prism stands on a base 6 cm equilateral triangle and its volume is $81\sqrt3$ cm3. The height (in cm) of the prism is:
Option 1: 9
Option 2: 10
Option 3: 12
Option 4: 15
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Correct Answer: 9
Solution :
The base of a right prism = 6 cm
Volume $= 81\sqrt3$ cm
3
Area of base of prism $= \frac{\sqrt{3}}{4}×6×6 = 9\sqrt{3}$ cm
2
Volume of a right prism = area of base × height
⇒ $81\sqrt3=9\sqrt{3}$ × height
⇒ Height = 9 cm
Hence, the correct answer is 9.
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