Question : The base of a pyramid is an equilateral triangle of side 10 m. If the height of the pyramid is $40 \sqrt{3}$ m, then the volume of the pyramid is:
Option 1: 1,000 m3
Option 2: 1,200 m3
Option 3: 9,00 m3
Option 4: 8,00 m3
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Correct Answer: 1,000 m 3
Solution :
Given: The base of a pyramid is an equilateral triangle of side 10 m.
The height of the pyramid is $40 \sqrt{3}$ m.
Use the formulas,
The volume of the pyramid = $\frac{1}{3}\times (\text{The area of the base})\times (\text{Height})$,
The area of the equilateral triangle = $\frac{\sqrt{3}}{4}\times (\text{side})^2$
The area of the equilateral triangle = $\frac{\sqrt{3}}{4}\times {10}^2=25\sqrt3$ m
2
The volume of the pyramid = $\frac{1}{3}\times 25\sqrt3 \times 40\sqrt3=1000$ m
3
Hence, the correct answer is 1,000 m
3
.
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