What is the height of the smaller model in this statue scaling problem?

[Payne0511]

Homework Statement

A statue is to be 'scaled down.' It will have its size changed without changing its shape. It starts with an initial volume of 4.25 m^3 and ends up with a final volume of 0.250 m^3.

If the height of the original statue was 215 cm, calculate the height of the smaller model.

Homework Equations

no clue

The Attempt at a Solution

I am assuming there has to be some sort of proportionality to this. the volume is shrinking to 1/17th the original size. the height is only one of the three dimensions that make up the volume. so there must be someway to use that to figure this out, but I have no idea.

thanks

 

[rl.bhat]

Find the cube root of 1/17. That into the original height of the statue will be the new height of the smaller statue.

 

[tomcue]

for any help

I would approach this problem by first understanding the concept of scale and proportionality. In this case, we know that the volume of the original statue is 4.25 m^3 and the final volume is 0.250 m^3. This means that the final volume is 1/17th of the original volume. We can use this information to find the scale factor between the two statues.

The scale factor can be calculated by taking the cube root of the ratio of the final volume to the original volume. In this case, the scale factor is ∛(0.250/4.25) = 0.5. This means that the smaller model is half the size of the original statue in all three dimensions.

Now, we can use this scale factor to find the height of the smaller model. Since we know that the original statue was 215 cm tall, we can simply multiply this by the scale factor of 0.5 to get the height of the smaller model. The height of the smaller model would be 215 cm x 0.5 = 107.5 cm.

In conclusion, the height of the smaller model is 107.5 cm. This approach can be applied to any scale problem where the shape remains the same but the size changes. It is important to understand the concept of scale and proportionality to solve such problems.