the edge of a cube is increased by 20%.Find the percentage increase in the surface area of the cube
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Let the edge of the cube(a) be 6 cm
Then total surface area = 6a cm ^2
= 6×6^2 cm^2
= 6×36 cm^2
=216 cm^2
by increasing 20% edge of the cube ,edge =6+20/100×6
=7.2 cm
then total surface area =6× 7.2^2 cm^2
=311.04 cm^2
let increase in total surface area be x%
then,
216+x/100×216=311.04
=>216x/100=311.04-216
=>x= 95.04×100/216
=>x=44
Hence the increased percentage of the total surface area is 44% .
you can also let variable for Cube's edge instead of number
Then total surface area = 6a cm ^2
= 6×6^2 cm^2
= 6×36 cm^2
=216 cm^2
by increasing 20% edge of the cube ,edge =6+20/100×6
=7.2 cm
then total surface area =6× 7.2^2 cm^2
=311.04 cm^2
let increase in total surface area be x%
then,
216+x/100×216=311.04
=>216x/100=311.04-216
=>x= 95.04×100/216
=>x=44
Hence the increased percentage of the total surface area is 44% .
you can also let variable for Cube's edge instead of number
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