When an object gets larger, why does the volume of an object increase faster than the surface area?

Physics

1 answer:

alina1380 [7]3 years ago

6 0

Let us consider the object to be a cell.

Explanation:

As a cell grows bigger, its internal volume enlarges and the cell membrane expands. This results in the increase in volume more rapidly than does the surface area, and so the relative amount of surface area available to pass materials to a unit volume of the cell steadily decreases. This means the surface area to the volume ratio gets smaller as the cell gets larger.

Example of a cube:

Cube size Surface area Volume

2cm 2 × 2 × 6 = 24 cm² 2 × 2 × 2 = 8 cm³

4 cm 4 × 4 × 6 = 96 cm² 4 × 4 × 4 = 64 cm³

6 cm 6 × 6 × 6 = 216 cm² 6 × 6 × 6 = 216 cm³

8 cm 8 × 8 × 6 = 384 cm² 8 × 8 × 8 = 512 cm³

This shows as the object gets larger, the volume of an object increases faster than the surface area.

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An automobile traveling 95 km/h overtakes a 1.30-km-long train traveling in the same direction on a track parallel to the road.

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Answer:

Same direction: t=234s; d=6.175Km

Opposite direction: t=27.53s; d=0.73Km

Explanation:

If the automobile and the train are traveling in the same direction, then the automobile speed relative to the train will be $v_{AT}=v_A-v_T$ (the train must see the car advancing at a lower speed), where $v_A$ is the speed of the automobile and $v_T$ the speed of the train.

So we have $v_{AT}=(95km/h)-(75Km/h)=20Km/h$ .

So the train (anyone in fact) will watch the automobile trying to cover the lenght of the train L at that relative speed. The time required to do this will be:

$t = \frac{L}{v_{AT}} = \frac{1.3Km}{20Km/h} = 0.065h=234s$

And in that time the car would have traveled (relative to the ground):

$d=v_At=(95Km/h)(0.065h)=6.175Km$

If they are traveling in opposite directions, we have to do all the same but using $v_{AT}=v_A+v_T$ (the train must see the car advancing at a faster speed), so repeating the process: