Subject: weight

Name: Sarah

Who is asking: Teacher
Level: Secondary

Question: Hi,

I was hoping that you could answer these question:

A regular-sized brick weighs 4 kilograms. How much will a similar toy brick, made of the same material, but all of the same dimensions of which are four times smaller, weigh?

The 300-metre tall Eiffel tower is made of steel and weighs 8 000 000 kg. An exact replica, made of the same material, weighs 1 kg. How high is the replica

Thanks in advance!

Hi Sarah,

Imagine that you are going to make the toy brick by cutting up the real brick.

First cut off one-quarter of the length of the brick. Call this piece slice 1. Slice 1 is one-quarter of the whole brick so it weights  1/4 x 4 kg.

Next slice off one-quarter of the height of slice 1. Call this piece slice 2.

Slice 2 weighs one-quarter of the weight of slice 1, that is its weight is  1/4 x  1/4 x 4 kg.

Finally take slice 2 and cut one-quarter off its depth. Call this piece slice 3.

Slice 3 is one-quarter of slice 2 so its weight is  1/4 x  1/4 x  1/4 x 4 kg.

Slice 3 is one-quarter as long, one-quarter as high and one-quarter as deep as the original brick so this is the toy brick you wanted.

For the second problem, suppose that the replica is  1/a times the height of the real tower. Now can you do the second problem?

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