知识点 5
Solve for a missing dimension given area/surface area/volume information.
Use the area or volume formula to work backward from a given measure to the missing length.
核心知识
When a problem gives you area or volume and asks for a length, set up the formula, plug in what you know, and solve for the missing dimension.
深入理解
Rule: Work backward from the given area or volume to the missing length.
- Substitute the known values.
- Isolate the variable.
- Check whether the question wants the raw variable or a related value like diameter.
The algebra is usually simple; the key is reporting the right dimension.
分步讲解
- Write the relevant formula (area, surface area, or volume).
- Substitute every known value.
- Solve for the remaining variable.
- Re-read the question: does it ask for that variable, or something derived from it (like diameter from radius)?
常见误解
- Finding the radius but reporting it as the diameter (or vice versa).
- Forgetting to take the square root after isolating
𝑟 2 - Solving for height when the question asks for slant height, which requires the Pythagorean theorem.
题目
示例解析
A sphere has a volume of
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