Q1. What property remains constant during conversion of solids?
✔ Only volume is conserved when a solid is melted and recast into another shape.
Q2. Which formula represents the volume of a sphere?
✔ The standard formula for the volume of a sphere is four-thirds pi r cubed.
Q3. In the example, what was the calculated height of the cone?
✔ Using the volume conservation rule with given radii, the height calculates to fifty-four centimeters.
Show transcript
[Slide 1] Understanding Conversion of Solids
When solids are melted and recast, their volume remains constant. Only the shape changes while the material amount stays identical. Think of melting a wax candle into a new mold.
[Slide 2] The Golden Rule
The core principle is that the initial volume equals the final volume. You must use standard formulas for each shape involved. Equate them to find the unknown dimension.
[Slide 3] Worked Example Setup
Consider a sphere of radius 6 cm melted into a cone. The cone has a base radius of 4 cm. We need to calculate the height of this new cone.
[Slide 4] Solving for Height
Cancel common terms like pi and three from both sides. Substitute the radius values into the simplified equation. You will find the height is fifty-four centimeters.
[Slide 5] Common Mistake Alert
Students often mistakenly equate surface areas instead of volumes. Remember, only volume is conserved during melting. Always check that your units match before solving.
[Slide 6] Quick Recap
To summarize, volume is conserved when solids are recast. Identify the shapes and apply their specific formulas accurately. Practice various combinations to master this topic.