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

See explanation below

Explanation:

Supose #l# the side lengthof cube

The 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%#