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A metal bar can be melted down to form 320 solid ornaments of height 2.8cm, how many similar ornaments of height 11.2cm could have been formed by the same metal bar?

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(Original post by

A metal bar can be melted down to form 320 solid ornaments of height 2.8cm, how many similar ornaments of height 11.2cm could have been formed by the same metal bar?

**CresentHan**)A metal bar can be melted down to form 320 solid ornaments of height 2.8cm, how many similar ornaments of height 11.2cm could have been formed by the same metal bar?

With that 896cm, you want to make 11.2cm tall ornaments.

896 / 11.2 = 80 ornaments(11.2cm)

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(Original post by

So the total height of all the ornaments will be 2.8cm x 320 = 896 cm

With that 896cm, you want to make 11.2cm tall ornaments.

896 / 11.2 = 80 ornaments(11.2cm)

**lyamlim97**)So the total height of all the ornaments will be 2.8cm x 320 = 896 cm

With that 896cm, you want to make 11.2cm tall ornaments.

896 / 11.2 = 80 ornaments(11.2cm)

To work out the scale factor -> 2.8/11.2. This gives 0.25. So we know the proportion between the height of the ornaments is 0.25

Therefore to find how many ornaments 11.2cm will make, we do 320 * 0.25(because it is similar so you can work out the how many ornaments there are).

However I quite like your method, but is algebraic?

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#4

(Original post by

An alternative is to work out the scale factor between the height of the ornaments(because they are similar).

To work out the scale factor -> 2.8/11.2. This gives 0.25. So we know the proportion between the height of the ornaments is 0.25

Therefore to find how many ornaments 11.2cm will make, we do 320 * 0.25(because it is similar so you can work out the how many ornaments there are).

However I quite like your method, but is algebraic?

**theBranicAc**)An alternative is to work out the scale factor between the height of the ornaments(because they are similar).

To work out the scale factor -> 2.8/11.2. This gives 0.25. So we know the proportion between the height of the ornaments is 0.25

Therefore to find how many ornaments 11.2cm will make, we do 320 * 0.25(because it is similar so you can work out the how many ornaments there are).

However I quite like your method, but is algebraic?

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#5

(Original post by

Yeah, didnt think of that. Yep its algebraic, I like to do things that way.

**lyamlim97**)Yeah, didnt think of that. Yep its algebraic, I like to do things that way.

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#6

When considering mathematical similarity of 3D objects you have to consider that it will be stretched in 3 dimensions. So if the larger object is 4 times taller it would be 4x4x4 greater volume.

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Posted from TSR Mobile

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#7

**CresentHan**)

A metal bar can be melted down to form 320 solid ornaments of height 2.8cm, how many similar ornaments of height 11.2cm could have been formed by the same metal bar?

Bars are similar and three-dimensional, hence we need to find the volume scale factor. This is the same as the length scale factor cubed.

Volume scale factor = (1/4)^3 = 1/64

320 * 1/64 = 320/64 = 5 ornaments

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#9

(Original post by

Which one is correct?

**CresentHan**)Which one is correct?

(Original post by

The length scale factor is 2.8/11.2 = 1/4 (= 0.25)

Bars are similar and three-dimensional, hence we need to find the volume scale factor. This is the same as the length scale factor cubed.

Volume scale factor = (1/4)^3 = 1/64

320 * 1/64 = 320/64 = 5 ornaments

**OscarTG**)The length scale factor is 2.8/11.2 = 1/4 (= 0.25)

Bars are similar and three-dimensional, hence we need to find the volume scale factor. This is the same as the length scale factor cubed.

Volume scale factor = (1/4)^3 = 1/64

320 * 1/64 = 320/64 = 5 ornaments

Isn't there a markscheme for this question?

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#12

**lyamlim97**)

So the total height of all the ornaments will be 2.8cm x 320 = 896 cm

With that 896cm, you want to make 11.2cm tall ornaments.

896 / 11.2 = 80 ornaments(11.2cm)

**lyamlim97**)

Yeah, didnt think of that. Yep its algebraic, I like to do things that way.

**OscarTG**)

The length scale factor is 2.8/11.2 = 1/4 (= 0.25)

Bars are similar and three-dimensional, hence we need to find the volume scale factor. This is the same as the length scale factor cubed.

Volume scale factor = (1/4)^3 = 1/64

320 * 1/64 = 320/64 = 5 ornaments

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