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?
Penny