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

Question :-

by what percent does the volume of a cube increase if the length of each edge is is increased by 50% ?

Solution :-

What to find here ?

we have to find here the percent of the volume of cube which was increased .

How to find it ?

we can find it by taking the length of each edge of a cube x unit and finding the new length and volume then we have to find the increase volume then by giving the formula of percentage of increase volume we can find the answer easily !

Answer :-

the initial volume of a cube is a^3 (a= side of the cube )

final volume = (3a/2)^3=(27a^3/8)

since each edge length is increased by 50% .

so we have to find the percent of increase in volume ;

Formula to be used ;

(increase in volume/ initial value) X 100

(((27/8-1) a^3)/a^3)×100

= (19/8)×100

= 237.5%

hence the increase volume of the cube is 237.5% .