Question

each edge of a cube is increased by 50% .find the %increase in the TSA​

Answer 1

Answer:

T.S.A of cube is 125

Step-by-step explanation:

Let x be the edge of a cube.

Surface area of the cube having edge x = 6x2 ………..(1)

As given, a new edge after increasing the existing edge by 50%, we get

The new edge = x + 50 x /100

The new edge = = 3x/2

Surface area of the cube having edge 3x/2 = 6 x (3x/2)2= (27/2)x2……..(2)

Subtract equation (1) from (2) to find the increase in the Surface Area:

Increase in the Surface Area = (27/2)x2 – 6x2

Increase in the Surface Area = = (15/2)x2

Now,

Percentage increase in the surface area = ((15/2)x2 / 6x2) x 100

= 15/12 x 100

= 125%

Therefore, the percentage increase in the surface area of a cube is 125.

Answer 2

Answer:

let each side length is=a cm

TSA 6a^2

then now according to the question

each edge is increased by 50%

then 50/100×a =a/2

now new length of each side is a/2

TSA= 6(length of the side)^2

= 6(a/2)^2

=6×a^2/4

=3a^2/2 cm^2

then now by what percent the new TSA was increased

= 25% is increased

you can check also by adding 25% in the first TSA for confirmation

let's check

first TSA is 6a^2

6a^2×25/100

6a^2×1/4 = 3a^2/2 cm^2

hope it helps you Chelli