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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!

divy3993
  • 177

1 Answers1

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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

divy3993
  • 177