Question

. 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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Answer 1

The smaller bottle holds 12.5 ml of perfume.

I solved it and came with this result.

Answer 2

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:

• 
  `k = 5/10 = 1/2`

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

• 
  `V_(small)/V_(large) = k^3\\`

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

• 
  `V_(small)/100= (1/2)^3\\`
• 
  `V_(small)/100= 1/8`
• 
  `V_(small)= 1/8*100=12.5`

The smaller bottle holds 12.5 ml of perfume.