To determine how many such sheets are needed to reach a height of 30 cm, we need to follow these steps:
1. Understand the given values:
- The thickness of each sheet of metal is [tex]\(\frac{5}{8}\)[/tex] cm thick.
- The desired total height of the stack of sheets is 30 cm.
2. Convert the fraction to a decimal: The thickness of each sheet is given as a fraction. First, let's convert [tex]\(\frac{5}{8}\)[/tex] to a decimal:
[tex]\[
\frac{5}{8} = 0.625 \text{ cm}
\][/tex]
3. Set up the equation:
- We need to find out how many sheets (let's denote this number as [tex]\(n\)[/tex]) of 0.625 cm thickness each are required to make up the total height of 30 cm.
- Mathematically, this can be represented as:
[tex]\[
n \times 0.625 \text{ cm} = 30 \text{ cm}
\][/tex]
4. Solve for [tex]\(n\)[/tex]:
- To find [tex]\(n\)[/tex], we need to isolate [tex]\(n\)[/tex] on one side of the equation. This is done by dividing the total height by the thickness of one sheet:
[tex]\[
n = \frac{30 \text{ cm}}{0.625 \text{ cm}}
\][/tex]
5. Perform the division:
- Calculating the above expression gives:
[tex]\[
n = \frac{30}{0.625} = 48 \text{ sheets}
\][/tex]
Thus, you need 48 sheets of metal, each [tex]\(\frac{5}{8}\)[/tex] cm thick, to reach a height of 30 cm.
