Answer:
Option 2 - [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Given : The radius of one sphere is twice as great as the radius of a second sphere.
To find : The ratio of their surface areas?
Solution :
The surface area of the sphere is [tex]A=4\pi r^2[/tex]
Let, the radius of one sphere is r
The surface area of one sphere is [tex]A_1=4\pi r^2[/tex]
Radius of second sphere is R
The surface area of second sphere is [tex]A_2=4\pi R^2[/tex]
According to question,
The radius of one sphere is twice as great as the radius of a second sphere.
i.e, r=2R
Now, The ratio of their surface areas is
[tex]Ratio=\frac{A_2}{A_1}[/tex]
[tex]Ratio=\frac{4\pi R^2}{4\pi r^2}[/tex]
Substitute r=2R,
[tex]Ratio=\frac{4\pi R^2{4\pi (2R)^2}}[/tex]
[tex]Ratio=\frac{4\pi R^2}{16\pi R^2}[/tex]
[tex]Ratio=\frac{1}{4}[/tex]
Therefore, Option 2 is correct.
The ratio of their surface area is [tex]\frac{1}{4}[/tex]
