An edge of a cube is increase by 10%.Find the percentage by which the surface area of the cube increases ? plz explain
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Let the original edge of the cube be a
now the edge is increased by 10%
10% of a = 10/100 × a
= a/10
so the new cube edge = a/10 + a = 11a/10 =1.1 a
The surface area of the original cube = 6a²
and the surface area of new cube = 6 a² = 6× (1.1a)²
= 6 × 1.21 a²
= 7.26 a²
now the percentage increase in the surface area
new surface area - original surface area /original surface area × 100
= 7.26 a² - 6a² / 6a² × 100
= 1.26a²/6a² × 100
= 1.26 / 6 × 100
= 0.21 × 100
= 21 %
now the edge is increased by 10%
10% of a = 10/100 × a
= a/10
so the new cube edge = a/10 + a = 11a/10 =1.1 a
The surface area of the original cube = 6a²
and the surface area of new cube = 6 a² = 6× (1.1a)²
= 6 × 1.21 a²
= 7.26 a²
now the percentage increase in the surface area
new surface area - original surface area /original surface area × 100
= 7.26 a² - 6a² / 6a² × 100
= 1.26a²/6a² × 100
= 1.26 / 6 × 100
= 0.21 × 100
= 21 %
Answered by
3
Let the original edge of the cube be "a"
now the edge is increased by 10%
10% of a = a/10
so the new cube edge = a/10 + a =1.1 a
The surface area of the original cube = 6a²
and the surface area of new cube = 6 a² = 6× (1.1a)²
= 7.26 a²
now the percentage increase in the surface area
new surface area - original surface area /original surface area × 100
= 7.26 a² - 6a² / 6a² × 100
= 1.26a²/6a² × 100
= 1.26 / 6 × 100
= 21 %
now the edge is increased by 10%
10% of a = a/10
so the new cube edge = a/10 + a =1.1 a
The surface area of the original cube = 6a²
and the surface area of new cube = 6 a² = 6× (1.1a)²
= 7.26 a²
now the percentage increase in the surface area
new surface area - original surface area /original surface area × 100
= 7.26 a² - 6a² / 6a² × 100
= 1.26a²/6a² × 100
= 1.26 / 6 × 100
= 21 %
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