Two cuboids have the same volume. Their length are in the ratio 5 : 4 and their breadth are in the ratio 2 : 3. Find the ratio of their heights.Options5 : 66 : 54 : 55 : 4
Question
Two cuboids have the same volume. Their length are in the ratio 5 : 4 and their breadth are in the ratio 2 : 3. Find the ratio of their heights.Options5 : 66 : 54 : 55 : 4
Solution
The volume of a cuboid is given by the formula: Volume = Length × Breadth × Height.
Given that the two cuboids have the same volume, we can set up the following equation:
(5x) * (2y) * h1 = (4x) * (3y) * h2
Simplify the equation:
10xy * h1 = 12xy * h2
Divide both sides by xy:
10h1 = 12h2
Divide both sides by 10:
h1 = 1.2h2
Therefore, the ratio of their heights is 1.2 : 1, or simplified to 6 : 5. So, the correct option is 6 : 5.
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