How Do You Maximize the Volume of a Prism with an Equilateral Triangle Base?

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SUMMARY

The discussion focuses on maximizing the volume of a prism with an equilateral triangle base, where the total edge length is 18 cm. The optimal side length of the triangle is determined to be 6 cm, leading to a maximum volume of 36√3 cm³, which is approximately 62.35 cm³ when rounded to two decimal places. Participants emphasize the importance of applying geometric principles and formulas to solve the problem effectively.

PREREQUISITES
  • Understanding of geometric principles related to prisms
  • Knowledge of equilateral triangle properties
  • Familiarity with volume calculation formulas
  • Basic algebra for solving equations
NEXT STEPS
  • Study the formula for the volume of a prism: V = Base Area × Height
  • Learn how to derive the area of an equilateral triangle
  • Explore optimization techniques in calculus
  • Investigate geometric constraints in multi-dimensional shapes
USEFUL FOR

Students studying geometry, educators teaching mathematical optimization, and anyone interested in solving real-world problems involving geometric shapes.

rachael
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3 The cross-section of a solid prism is an equilateral triangle, The sum of the lengths of the edges of the prsim is 18 cm.
a. find the exact side length of the triangle in cm so that the volume is maximised.
b. Find the maximum volume in cm^3, correct to 2dp

i can't seem to find the correct answer for this question
could anyone please help me?
thank you
 
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rachael said:
3 The cross-section of a solid prism is an equilateral triangle, The sum of the lengths of the edges of the prsim is 18 cm.
a. find the exact side length of the triangle in cm so that the volume is maximised.
b. Find the maximum volume in cm^3, correct to 2dp

i can't seem to find the correct answer for this question
could anyone please help me?
thank you
wheres ur working?
 

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