A cube of each side 'a' is elongated in such a way that one side is increased by 20% while the other two sides arereduced by 5% and x% respectively. Calculate the value of 'x' and change in the total surface area
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x = 12.28 & 0.87% change in the total surface area when cube is elongated 20% increase in one side & 5 & x % decrease in two sides
Step-by-step explanation:
A cube of each side 'a
Volume = a³
Surface Area = 6a²
One side increased by 20 % = a + (20/100)a = 1.2a
second side reduced by 5 % = a - (5/100)a = 0.95a
Third Side = a - (x/100)a = a (1 - x/100)
Equating Volume
1.2a * 0.95a * a (1 - x/100) = a³
=> 1 - x/100 = 1/1.14
=> x/100 = 1 - 1/1.14
=> x/100 = 0.14/1.14
=> x = 14/1.14
=> x = 12.28 %
x = 12.28
Sides are 1.2a , 0.95a & a/1.14
Surface area = 2 ( 1.2a * 0.95a + 1.2a * a/1.14 + 0.95a * a/1.14)
= 2a² ( 1.2996 + 1.2 + 0.95) /1.14
= 6.052a²
increase in surface Area = 6.052a² - 6a²
= 0.052a²
% increase in surface Area = (0.052a²/6a²)* 100 = 0.87%
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