Question

By what percent does the volume of a cube increase, if the lenght of each edge is increased by 50% ?​

Answer 1

Answer:

$\huge\underline\bold {Answer:}$

Let each edge of the cube be x cm.

Then, volume of the cube =

$x {}^{3} \: cm {}^{3}$

Length of the edge after increase = 150/100 x cm = 1.5x cm.

Therefore, increased volume

$= (1.5x) {}^{3} \: cm \\ 3.375 {x}^{3} cm {}^{3}$

Therefore % increase

$= (3.375 {x}^{3} - x {}^{3} ) \div {x}^{3}$

$= (2.375 \times 100)\% = 237.5\%$

Answer 2

Answer:

Let the edge of cube be l

∴ volume of cube =l

3

If the length of each edge was increased by 50%, then the edge of cube would have been 1.5l

∴ volume of new cube =(1.5l)

3

=3.375l

3

∴ percent increase in volume =

l

3

3.375l

3

−l

3

=2.375×100=237.5%