Question

if side of cube decreases by 10% what is the %change in total surface area

Answer 1

Let the side of the cube be x
Total surface area = 6x²
% of decrease in side = 10%
Decreased side = x - (10/100)× x
= x -   x/10
= (10x -x)/10
= 9x/10
New total surface area = 6(9x/10)²
= 6(81x²/100)
= 243x²/50
Difference/ change in total surface areas = 6x² -  243x²/50
= 300x² - 243x²/50
= 57x²/50
% of change in total surface area = [(57x²/50)6x²] × 100
= [57/(50×6)]× 100
= [57/300]× 100
= 57/3
= 19%
∴ The % change in Total surface area is 19%