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Question
If each edge of a cube is increased by 50%, the percentage increase in its surface area is
Options
50%
75%
100%
125%
Solution
Let,
a →a Initial edge of the cube
A → Initial surface area of the cube
a' → Increased edge of the cube
A' → Increased surface area of the cube
We have to find the percentage increase in the surface area of the cube
Since it’s given that
`a = a+axx50/100`
`= 3/2 a`
We have,
`A' = 6(a)^2`
`= 6 (3/2a)^2 { Since , a' = 3/2 a}`
` = 9/4 (6a^2)`
` =9/4 A`
Percentage increase in surface area,
`=(A'-A)/A xx 100`
`=(9/4 A-A)/A xx 100`
`=(5/4A)/A xx 100`
= 125
Increase in surface area is 125% .
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