The Height of a Monument Is $20 \mathrm {~m}$ a Horizontal Cross-Section at a Distance

question 158

Multiple Choice

The height of a monument is $20 \mathrm {~m}$ . A horizontal cross-section at a distance $x$ meters from the top is an equilateral triangle with side $\frac { x } { 4 }$ meters. Find the volume of the monument. Select the correct answer.

• A) \(\frac { 125 \sqrt { 3 } } { 3 } \mathrm {~m} ^ { 3 }\)
• B) \(\frac { 125 \sqrt { 2 } } { 3 } \mathrm {~m} ^ { 3 }\)
• C) \(\frac { \sqrt { 3 } } { 3 } \mathrm {~m} ^ { 3 }\)
• D) \(\frac { 125 \sqrt { 2 } } { 2 } \mathrm {~m} ^ { 3 }\)
• E) \(125 \sqrt { 3 } \mathrm {~m} ^ { 3 }\)