I would like to know the approach for followings:
Que 1:
Volume of Cube is increased by $72.8$%, determine the % increase, in the side of the cube.
My Approach:
Step 1: Volume of Cube = $a^3$
Step 2: Volume increased by $72.8$% $= a^3 + 0.728a^3 = 1.728a^3$.
Don't know further
I know the answer but don't know the approach. Help me!
Ans: $20$%
Que 2:
Area of Square is decreased by $19$%, determine the % decrease, in the side of the square.
My Approach:
Step 1: Area of Square = $a^2$
Step 2: Area decreased by $19$% $= a^2 – 0.19a^2 = 0.81a^3$.
Don't know further
I know the answer but don't know the approach. Help me!
Ans: $10$%
Thank You!
Best Answer
Ans 1:
Volume of Cube $ = a^3$
Increase in volume by $72.8$% $= a^3 + 0.728a^3 = 1.728a^3$
Now, Finding side of Cube $= \sqrt[3]{1.728a^3} = 1.2a$
Now Increase in sides $= 1.2a - a = 0.2a$
So $0.2$ times increase in sides of cube. Hence $0.2$ in % = $0.2 * 100 = 20$%.
Thus $20$% increase in side of the cube
Ans 2:
Area of Square $ = a^2$
Decrease in Area by $19$% $= a^2 - 0.19^2 = 0.81a^2$
Now, Finding side of Square $= \sqrt[2]{0.81a^2} = 0.9a$
Now Decrease in sides $= a - 0.9a = 0.1a$
So $0.1$ times decrease in sides of square. Hence $0.1$ in % = $0.1 * 100 = 10$%.
Thus $10$% decrease in side of square