Question related two different ways to do solution

Thread starter helloword365
Start date Apr 12, 2025

Click For Summary

SUMMARY

The discussion centers on a mathematical problem involving the calculation of the sidelength of a cross-section, specifically expressed as 8 - 8x/3. The user questions the validity of this expression compared to their own method, which relies on similar triangle relationships. The two potential energy values in question are 470 kJ and 117 kJ. The user seeks clarification on the correctness of the integral presented in red font.

PREREQUISITES

Understanding of calculus, specifically integration techniques.
Familiarity with geometric concepts, particularly similar triangles.
Knowledge of energy calculations in physics.
Experience with mathematical notation and expressions.

NEXT STEPS

Review integration techniques for calculating areas under curves.
Study the properties of similar triangles and their applications in geometry.
Explore energy conservation principles in physics.
Investigate common errors in mathematical problem-solving and verification methods.

USEFUL FOR

Students in mathematics or physics, educators teaching calculus and geometry, and anyone involved in solving complex mathematical problems.

Apr 12, 2025

helloword365

Homework Statement: An upside-down square pyramid with a height of 3 m and side lengths of 8m is filled to the brim with water. How much work is needed to lift all the water out of the container through the top. (ρ = 1000 kg/m3, g = 9.8 m/s2)

Relevant Equations: Work = Force * displacement

My work:

Answer Key (red font one) *may not be right.

My question is why is sidelength of cross section written as 8-8x/3, while my way of doing it doesn't involve that (involves suspicious similar triangle relationships)? Which answer (if any) is right here? 470 kj or 117 kj? Thank you!