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Question
The ratio between the lengths of the edges of two cubes is in the ratio 3: 2. Find the ratio between their:
(i) total surface area
(ii) volume.
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Solution
Ratio in edges of two cubes = 3:2
Let edge of first cube = 3x
Then edge of second cube = 2x
(i) Now total surface area of first cube = 6 x (3x)2 = 6 x 9x2 = 54x2
and of surface area of second cube = 6 x (2x)2 = 6 x 4x2 = 24x2
Ratio = 54x2: 24x2 = 9:4
(ii) Volume of first cube = (3x)3 = 27x3
and second cube = (2x)3 = 8x3
Ratio = 27x3: 8x3 = 27 :8
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