A rectangular block of lead 35 cm long and 28 cm wide, is melted and recast into cubes of edge 4cm. 200 cm3 of lead is lost in the process. 150 cubes are obtained. Calculate the height of the rectangular block before it was melted 

Let's solve this step-by-step using the information provided:

1. **Find the volume of the rectangular block:**

   Let the height of the rectangular block be \( h \). Given the length and width of the block:
   - Length = 35 cm
   - Width = 28 cm

   The volume of the rectangular block is:
   \[
   V_{\text{block}} = \text{length} \times \text{width} \times \text{height} = 35 \times 28 \times h
   \]

2. **Find the total volume of the cubes produced:**

   Each cube has an edge length of 4 cm, so the volume of one cube is:
   \[
   V_{\text{cube}} = 4^3 = 4 \times 4 \times 4 = 64 \, \text{cm}^3
   \]

   Since 150 cubes are obtained, the total volume of these cubes is:
   \[
   V_{\text{total cubes}} = 150 \times 64 = 9600 \, \text{cm}^3
   \]

3. **Account for the volume of lead lost:**

   We know that 200 cm\(^3\) of lead is lost in the process. Therefore, the original volume of the rectangular block must have been:
   \[
   V_{\text{block}} = V_{\text{total cubes}} + \text{volume lost}
   \]
   \[
   V_{\text{block}} = 9600 + 200 = 9800 \, \text{cm}^3
   \]

4. **Calculate the height of the rectangular block:**

   Using the expression for the volume of the block:
   \[
   9800 = 35 \times 28 \times h
   \]
   \[
   h = \frac{9800}{35 \times 28}
   \]
   \[
   h = \frac{9800}{980} = 10 \, \text{cm}
   \]

**The height of the rectangular block before it was melted was 10 cm.**

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### Related Questions
1. What is the formula to calculate the volume of a cube?
2. How do you convert a rectangular prism's dimensions into volume?
3. What happens to the volume when a shape is melted and reformed into another shape?
4. How do you handle situations where material is lost in a transformation process?
5. Can the shape of a rectangular block affect the volume?

### Tip
Always remember that when a solid is melted and recast, its total volume is conserved (minus any material losses).

A rectangular block of lead 35 cm long and 28 cm wide, is melted and recast into cubes of edge 4 cm. 200 cm³ of lead is lost in the process. 150 cubes are obtained. Calculate the height of the rectangular block before it was melted.

Solve a problem involving a rectangular block of lead that is melted and recast into cubes. Learn how to calculate the original height of the block using volume formulas, accounting for material loss. Suitable for students in Grades 8-10.

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