If the volume of a cube is increased by a factor of 10 (so that the new volume is 10 times the size of the original volume), by what factor does the surface area of the cube change?

surface area of cube time

Step-by-step explanation:

given data

new volume =  10 time original volume

to find out

what factor surface area change

solution

we consider here side of cube is a

and volume is V

we consider here a is 2

then volume will be v1 = a³ = 2³ = 8

and surface area = 6a²    = 6(2)² = 24    ..........1

so if volume increase 10 time

than

V = 10 × v1

a³ = 10 × 8

a³= 80

a = 2 × ∛10

and

surface area increase here

surface area = 6a²

surface area = 6( 2 × ∛10 )²

surface area = 24 ×    ............2

so from equation 1 and 2

surface area / surface area = 24 ×  / 24

surface area =

so here surface area of cube will be time

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step-by-step explanation:

1+2+3+4+5+6+7+8+9+10 = 55

2*10 = 20

55-20 = 35

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents