If the radius of a sphere is increased to twice its original size, what is the ratio of the new surface area to the original surface area, as well as the proportion of the new volume to the original volume?

Correct option is B

​Given :

Original radius of sphere = r
New radius = 2r

Formula Used :

Surface area of a sphere
S = $$4\pi r^2$$​​

Volume of a sphere
V $$= \frac{4}{3}\pi r^3$$​​

Solution :

(i) Surface Area Ratio

Original surface area:
S$$_1 = 4\pi r^2$$​​

New surface area:
​$$S_2 = 4\pi (2r)^2 = 16\pi r^2$$​​

​$$\text{Ratio } S_2 : S_1 = 16\pi r^2 : 4\pi r^2 = 4 : 1$$​​

(ii) Volume Ratio

Original volume
V$$_1 = \frac{4}{3}\pi r^3$$​​
New volume:

V$$_2 = \frac{4}{3}\pi (2r)^3 = \frac{32}{3}\pi r^3$$​​

Ratio V$$_2 : V_1 = 32 : 4 = 8 : 1$$​​

Answer :

Surface area ratio = 4 : 1

Volume ratio = 8 : 1