急(F.2 maths Rate and Ratio)20點

The sides of two cubes are in the ratio 4:5. Find the ratio of their total surface areas.

Method 1:
The two cubes are similar.
Hence, the ratio of their total surface areas
= 4² : 5²
= 16 : 25

Method 2:
Total surface area of a cube = 6 x (length of side)²
Hence, the ratio of their total surface areas
= (6 x 4²) : (6 x 5²)
= 16 : 25

Let 4x be a side of smaller square:

(4x)^2(6)/(5x)^2(6)

16x^2/25x^2

16/25

16:25

(4 x 4) x 6 : (5 x 5) x 6
16 x 6 : 25 x 6
96 : 150
48 : 75 <<< take out 2
16 : 25 <<< take out 3


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