Question

by what percentage the volume of a cube increases if the length of each edge is increased by 50%​ ​

Answer 1

Step-by-step explanation:

Given:-

The length of each edge is increased by 50%

To find:-

By what percentage the volume of a cube increases if the length of each edge is increased by 50%

Solution:-

Let the length of the cube be "a" units

Volume of the cube =a³ cubic units-----(1)

If length of the edge of the cube is increased by 50% then the edge o

f the cube becomes

=>a+50%of a

=>a+(50a)/100

=>a+a/2

=>(2a+a)/2

=>3a/2

Volume of the cube after increased =

=>(3a/2)³

=>27a³/8

=>(27/8)a³------(2)

Increased in the volume =27a³/8-a³

=>(27a²-8a³)/8

=>19a³/8

Now Increased percentage in the volume =(increasing volume/original volume)×100

=>(19a³/8)/a³)×100

=>(19/8)×100

=>(19×100)/8

=>(19×25)/2

=>475/2

=>237.5%

Answer:-

Increasing percentage in the volume is 237.5%