From the diagram, we know that the length of 3 small squares = length of 2 big squares.
And since Axel’s box is packed tightly to the brim without any gaps, it means that the height of the big squares and the small squares are the same.
In order for them to be the same, there must be 4 big squares on the left, and 9 small squares on the right.
Therefore, we can define 1 set = 4 big + 9 small.
For every set, there is (9-4) = 5 more small.
Qns states that there are 50 more small.
Therefore, there are (50/5) = 10 sets.
10 sets = 40 big + 90 small = 130 cubes altogether.
For (b),
We use 6u to represent length of 2 big or 3 small.
Therefore,
Length of 1 big = 3u
Vol of 1 big = 27 u^3
Length of 1 small = 2u
Vol of 1 small = 8 u^3
Since the volume of all big = volume of all small,
We need to find a common multiple between 27 and 8.
The simplest multiple = 27 * 8 = 216.
216 = 8 big = 27 small
Therefore, in terms of numbers, there are 8 units of Big cubes, and 27 units of Small cubes.
Total cubes = 8 + 27 =35 unites
Fraction of small cubes = 27/35
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i dont rlly understand q17. pls helpp thanksss 🙂
Hi Belinda!
Q17 is quite a challenging question.
For (a),
From the diagram, we know that the length of 3 small squares = length of 2 big squares.
And since Axel’s box is packed tightly to the brim without any gaps, it means that the height of the big squares and the small squares are the same.
In order for them to be the same, there must be 4 big squares on the left, and 9 small squares on the right.
Therefore, we can define 1 set = 4 big + 9 small.
For every set, there is (9-4) = 5 more small.
Qns states that there are 50 more small.
Therefore, there are (50/5) = 10 sets.
10 sets = 40 big + 90 small = 130 cubes altogether.
For (b),
We use 6u to represent length of 2 big or 3 small.
Therefore,
Length of 1 big = 3u
Vol of 1 big = 27 u^3
Length of 1 small = 2u
Vol of 1 small = 8 u^3
Since the volume of all big = volume of all small,
We need to find a common multiple between 27 and 8.
The simplest multiple = 27 * 8 = 216.
216 = 8 big = 27 small
Therefore, in terms of numbers, there are 8 units of Big cubes, and 27 units of Small cubes.
Total cubes = 8 + 27 =35 unites
Fraction of small cubes = 27/35
Hope these explanations helps!