## Question

###### If the side of cube is increased by 10%.what is the percentage increase in the volume of cube?

If the side of cube is increased by 10%.what is the percentage increase in the volume of cube?

## Answers

See explanation below

## Explanation:

Supose

#l# the side lengthof cubeThe volume is then

#V=l^3# If increase the length by 10%, the new length is

#l´=(1+10/100)·l=110/100·l#

#1+10/100=110/100# The new volume will be

#V´=l´^3=110^3/100^3·l^3=110^3/100^3V=1.331·V# The volume increase in percentage is 33,1%

#33.1%# ## Explanation:

#" the volume (V) of a cube is"#

#•color(white)(x)V=l^3#

#"where "l" is the side of the cube"#

#"assuming "l=1" unit"#

#"then "V=1^3=1" unit"^3#

#"increasing "l" by" 10%tol=1.1" units"#

#"then "V=(1.1)^3=1.331" units"^3#

#"an increase of "1.331-1=0.331#

#%"increase "=0.331xx100%=33.1%#

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