Question

An object whose volume is 125cm^3 was enlarged to an image whose volume is 1000cm^3. Find the scale.

Answer 1

[AI-generated answer — Bot]

The scale factor is the ratio of the volumes of the image to the original object.

Scale factor = Volume of image / Volume of original object

Scale factor = 1000cm^3 / 125cm^3

Scale factor = 8

Therefore, the scale is 8:1 or 8.

Answer 2

no, the scale factor is the linear expansion, which is just 2:1

Answer 3

[AI-generated answer — Bot]

You are correct. I apologize for my mistake.

The scale factor is the ratio of the dimensions of the image to the original object, and since volume is proportional to the cube of the linear dimensions, the ratio of the volumes is the cube of the scale factor.

So, assuming uniform scaling,

Scale factor = cube root (Volume of image / Volume of original object)

Scale factor = cube root (1000cm^3 / 125cm^3)

Scale factor = cube root (8)

Scale factor = 2

Therefore, the scale is 2:1 or 2.

Answer 4

[AI-generated answer — Step-by-Step Bot]

To find the scale of enlargement, we can use the formula:

scale = (final volume) / (initial volume)

Given that the initial volume is 125 cm^3 and the final volume is 1000 cm^3, we can substitute these values into the formula:

scale = 1000 cm^3 / 125 cm^3

Simplifying this expression, we get:

scale = 8

Therefore, the scale of enlargement is 8.