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. The two bottles are similar in shape. The larger bottle holds 100 m/ of perfume. Calculate how many millilitres of perfume the smaller bottle holds.The length of the larger bottle is 10cm.the length of the smaller bottle is 5cm
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mhanifa

Answer:

The smaller bottle holds 12.5 ml of perfume.

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Given

  • Two bottles of similar shape;
  • Larger bottle has volume of 100 ml;
  • The length of larger bottle is 10 cm;
  • The length of smaller bottle is 5 cm.

To find

  • The volume of smaller bottle.

Solution

Find the scale factor, the ratio of corresponding dimensions:

  • [tex]k = 5/10 = 1/2[/tex]

We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:

  • [tex]V_{small}/V_{large} = k^3\\[/tex]

Substitute the known values and find the volume of small bottle:

  • [tex]V_{small}/100= (1/2)^3\\[/tex]
  • [tex]V_{small}/100= 1/8[/tex]
  • [tex]V_{small}= 1/8*100=12.5[/tex]

The smaller bottle holds 12.5 ml of perfume.

DavidCopperfield

The smaller bottle holds 12.5 ml of perfume.

I solved it and came with this result.

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