Question

the diameter of the sphere is decreased by 50% what is the ratio between initial and final Curved surface area

Answer 1

surface area of sphere =4pi (radius)^2

=> 4pi (r)^2/4pi.(r/2)^2
=> 4/1
so ratio is 4:1
where r is initial radius of sphere (let)

Answer 2

Surface Area of Sphere(ar)

$= 4\pi {r}^{2}$

if diameter is decreased to 50%

$= > \frac{4\pi {r}^{2} }{4\pi {(\frac{r}{2})}^{2} } \\ = > \frac{4}{1}$

let the r is initial radius to Sphere

So, the ratio is 4:1

$\huge\fcolorbox{black}{white}{4 : 1}$