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

Question

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

Team Careers360 · Accepted Answer

Correct Answer: 1,000 m³

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 = $\frac{1}{3} imes ( ext{The area of the base}) imes ( ext{Height})$,
The area of the equilateral triangle = $\frac{\sqrt{3}}{4} imes ( ext{side})^2$
The area of the equilateral triangle = $\frac{\sqrt{3}}{4} imes {10}^2=25\sqrt3$ m²
The volume of the pyramid = $\frac{1}{3} imes 25\sqrt3 imes 40\sqrt3=1000$ m³
Hence, the correct answer is 1,000 m³.

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Question : The base of a pyramid is an equilateral triangle of side 10 m. If the height of the pyramid is 403 m, then the volume of the pyramid is:Option 1: 1,000 m3Option 2: 1,200 m3Option 3: 9,00 m3Option 4: 8,00 m3

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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