Question

Find the approximate change in the volume V of a cube of side x metre caused by increasing the side by 1%.​

Answer 1

Question :-- Find the approximate change in the volume V of a cube of side x metre caused by increasing the side by 1%. ?

Formula used :--

→ Volume of cube with sides x m is given by = x³ m³ .

Solution :--

It has been given given that side of cube is x m.

so,

→ initial volume of cube was = (x)³ m³ .

Now, side of cube was increased by 1% .

So,

→ New side of cube = x * (101)/100 = (1.01x) m [ As Total anything is 100% ] .

So,

→ New volume of cube with new increasing side will be = (1.01x)³ = (1.030301x³) m³

___________________

So,

→ Change in volume = 1.030301x³ - x³ = x³(1.030301 - 1) = x³(0.030301) m³

% change = (0.030301)x³ * 100 / x³ ( x³ will be cancel from both sides ) .

→ % change = 3.0301 %

Hence, their will be 3.0301% change in volume of cube when Each side is increased by 1 % .