Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
If the side of a cube is increased by 20%, find the percentage increase in its surface area.
40%
44%
48%
20%
44%
Use the net percentage change formula 2x+100x2тАЛ for area problems where the side increases by x. Here, 2(20)+100202тАЛ=40+4=44.
The side of a cube is increased by 20%.
Percentage┬аChange=x+y+100x├ЧyтАЛ
Use the net percentage change formula 2x+100x2тАЛ for area problems where the side increases by x. Here, 2(20)+100202тАЛ=40+4=44.
Many students incorrectly assume the percentage increase in surface area is the same as the side increase (20%) or multiply by 2 (40%), forgetting the square of the increase.
Define Surface Area Formula
The total surface area of a cube with side a is A=6a2. Since 6 is constant, the percentage change depends only on a2.
A=6a2
Apply Successive Percentage Increase
Since area is proportional to the square of the side (a├Чa), an increase of 20% applied twice follows the formula x+y+100xyтАЛ, where x=20 and y=20.
20+20+10020├Ч20тАЛ
Calculate Final Result
Summing the values: 40+100400тАЛ=40+4=44.
44%
B is correct because the successive increase of 20% on the area dimensions results in a net increase of 44%.
This same logic applies to circle area problems where radius increases (replace 20 with the radius change) and volume problems where you apply the formula for a third dimension.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants