What is the height of the smaller cylinder in this scale factor?

In summary, the conversation discusses the calculation of the height of a smaller cylinder based on the given information of two similar cylinders with different areas and heights. The scale factor for length is determined to be 4:10 and using this, the height of the smaller cylinder is calculated to be 5cm. The correctness of this calculation is confirmed by Mark.
  • #1
Gringo123
141
0
Can someone please tell me if I have done this correctly?

"2 cylinders are similar. The area of the ends of the smaller and larger cylinders are 16cm2 and 100cm2 respectively. The height of the larger cylinder is 12.5cm. Calculate the height of the smaller cylinder."

Firstly, if the scale factor for area is 16:100, am I right in saying that the scale factor to be used when calculating lenthgs would be 4:10?

proceding on that basis, the height of the smaller cylinder = 12.5 x 2 / 5 = 5cm.
 
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  • #2
Gringo123 said:
Can someone please tell me if I have done this correctly?

"2 cylinders are similar. The area of the ends of the smaller and larger cylinders are 16cm2 and 100cm2 respectively. The height of the larger cylinder is 12.5cm. Calculate the height of the smaller cylinder."

Firstly, if the scale factor for area is 16:100, am I right in saying that the scale factor to be used when calculating lenthgs would be 4:10?

proceding on that basis, the height of the smaller cylinder = 12.5 x 2 / 5 = 5cm.
Looks good to me.
 
  • #3
Thank you once again Mark!
 

1. What are area and length scale factors?

Area and length scale factors are mathematical tools used to scale and compare physical quantities such as distances, areas, and volumes. They are often used in scientific research to understand how phenomena change with size and to make accurate predictions at different scales.

2. How do area and length scale factors differ?

Area and length scale factors differ in the quantities they are used to scale. Length scale factors are used to compare distances or lengths, while area scale factors are used to compare areas or two-dimensional quantities. However, both scale factors follow the same mathematical principles.

3. What is the formula for calculating area scale factors?

The formula for calculating area scale factors is: SFarea = (Lnew/Loriginal)2, where SFarea is the area scale factor, Lnew is the new length or distance, and Loriginal is the original length or distance.

4. How are area and length scale factors used in scientific research?

Area and length scale factors are used in scientific research to understand how phenomena change with size. For example, scientists may use scale factors to compare the behavior of cells of different sizes or to predict the behavior of a large-scale system based on the behavior of a smaller-scale system.

5. What is the significance of area and length scale factors in engineering?

In engineering, area and length scale factors are crucial for designing and modeling structures and systems. By using scale factors, engineers can accurately predict how materials and structures will behave at different scales, allowing them to design structures that are safe and functional at any size.

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