Word problem-I would like to check my procedure

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The conversation is discussing how to set up an equation to relate the volume of a cube to its surface area. The equation for the volume of a cube is C=x^3, and the equation for its surface area is S=6x^2. Using the derivatives of these equations, the individual is trying to find a formula for x. The other person suggests solving for x in the surface area equation and substituting that into the volume equation. The final answer will involve x.]In summary, the conversation is focused on setting up an equation for the volume of a cube in terms of its surface area. The equations for volume and surface area are C=x^3 and S=6x^2, respectively. The individual is
  • #1
stanton
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word problem-Please help me to check my procedure

Homework Statement



A cubical ice block is melting at a rate that relates to its surface area. Set up an equation for the volume of a cube, C, in terms of its surface area, S.

Homework Equations



C=x^3
S=6x^2

The Attempt at a Solution




let length of the side of the cube:x
dC/dx=3x^2 dS/dx=12x dC/dS=x/4
Now what should I do? I think I did pretty well until now. How should I use this information for getting the answer? Or dC/dS(which is x/4) is the final answer?
 
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  • #2
You are almost half-way there, and this is not a calculus problem.

Work with S and find a formula for x.
 
  • #3
Thank you. But work with S? Would you mind if I want more specific explanation from you? Sorry, cause I am not very good at math, interpreting word problems.
 
  • #4
The problem said "Set up an equation for the volume of a cube, C, in terms of its surface area, S". That's why you need to "work with S".
You have [itex]C= x^3[/itex]. You also know that [/itex]S= 6x^2[/itex].

Solve [itex]S= 6x^2[/itex] for x (which is a length and so positive) and replace the "x" in [itex]C= x^3[/itex] with that/
 

What is a word problem?

A word problem is a mathematical question or puzzle that is presented in the form of words, rather than equations or symbols. It typically involves real-life situations and requires critical thinking and problem-solving skills to solve.

How do I solve a word problem?

To solve a word problem, you need to follow a step-by-step process that involves reading and understanding the problem, identifying the key information, choosing a strategy to solve it, and checking your answer to see if it makes sense.

What is the importance of checking my procedure in solving word problems?

Checking your procedure is crucial in solving word problems because it helps you catch any mistakes or errors you may have made. It also allows you to verify that your answer is correct and makes sense in the context of the problem.

What are some common strategies for solving word problems?

Some common strategies for solving word problems include drawing a diagram or picture, making a table or chart, using equations or formulas, and working backward from the given information.

How can I improve my skills in solving word problems?

To improve your skills in solving word problems, you can practice regularly, break down complex problems into smaller, more manageable parts, and seek help or guidance from a teacher or tutor. You can also try to understand and apply different problem-solving strategies.

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