Question

An increase in the radius of a galaxy by 10% increases its total surface area by 21%. ​
true or false and why

Answer 1

125%

true

I'm not sure to my answer but I believe in my self

Answer 2

answer is true

Step-by-step explanation:

Given:

Percentage increase of radius = 10%

Formula used:

Area of circle = πr2

Percentage change = {(Final value – Initial value)/Initial value} × 100

Calculation:

Let the Initial radius be r

Initial area = πr2

Increased radius = {(100 + 10)/100} × r = (1.1)r

⇒ New area = π(1.1r)2

Percentage increase = [{π(1.21r2) – πr2}/ πr2] × 100

⇒ Percentage increase = [πr2(1.21 – 1)/ πr2] × 100

⇒ Percentage increase = [1.21 – 1] × 100 = 21%

∴ The percentage increase in its area is 21%.