Question

Each edge of a cube is increased by 50 the percentage increase in the volume will be

Answer 1

Let the edge of cube be 'x'

$volume \: of \: cube \: = {x}^{3}$
Now each edge $\red{Increased\:by}$ 50%

Means
$x + x \times \frac{50}{100} \\ x + \frac{x}{2} \\ \frac{3x}{2}$
new edge of cube be 3x/2

So,
$new \: volume = { (\frac{3x}{2}) }^{3} \\ = \frac{27 {x}^{3} }{8}$

$percent \: increase = \frac{final \: volume - initial \: volume}{final \: volume} \times 100 \\ = \frac{ \frac{27 {x}^{3} }{8} - {x}^{3} }{ \frac{27 {x}^{3} }{8} } \times 100\\ = \frac{19 {x}^{3} }{27 {x}^{3} } \times 100 \\ \\ 70 \: percent$

$<b>$Percent increase is 70%

Answer 2

Answer:

125%

Step-by-step explanation

let the edge of cube be 'a'

surface area of cube =6a^2

increase in length of edge of cube=50%of 'a'

=50/100 x a

=a/2

new length= a + a/2= 3a/2

new surface area of cube 6a^2

=6x(3a/2)^2

6 x 9a^2/4

=27a^2/2

=increase in surface area= 27a^2/2 - 6a^2

=15a^2/2

percentage=(15a^2/2)/6a^2 x100 = 5/4 x 100 =150%

increase oin surface area = 150 %