Select the correct answerIf each edge of a cube is increased by 20%, find the percentage increase in its volume.Options68.860.888.8
Question
Select the correct answer
If each edge of a cube is increased by 20%, find the percentage increase in its volume.
Options
- 68.8
- 60.8
- 88.8
Solution
The volume of a cube is given by the formula V = a^3, where a is the length of an edge.
If each edge of the cube is increased by 20%, the new edge length is 1.20a.
The new volume V' is then (1.20a)^3 = 1.728a^3.
The increase in volume is V' - V = 1.728a^3 - a^3 = 0.728a^3.
To find the percentage increase, we divide the increase by the original volume and multiply by 100:
(0.728a^3 / a^3) * 100 = 72.8%.
So, none of the options given are correct. The correct answer should be 72.8%.
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