Star 'A' has twice the radius of star 'B'. The ratio of the surface area of star 'A' to the surface area of star 'B' is equal to
8
4pi
2
1/8
4
To determine the ratio of the surface area of star 'A' to the surface area of star 'B', we need to compare their surface areas. The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2,
where r is the radius of the sphere.
Given that star 'A' has twice the radius of star 'B', we can denote the radii as follows:
The radius of star 'A': r_A
The radius of star 'B': r_B
According to the problem, we have the relationship:
r_A = 2 * r_B.
Now let's calculate the surface areas of both stars.
The surface area of star 'A' is given by:
Surface Area_A = 4π * r_A^2.
The surface area of star 'B' is given by:
Surface Area_B = 4π * r_B^2.
Using the relationship r_A = 2 * r_B, we substitute it into the equations:
Surface Area_A = 4π * (2 * r_B)^2 = 4π * 4 * r_B^2 = 16π * r_B^2.
Surface Area_B = 4π * r_B^2.
Now, let's find the ratio of the two surface areas:
R = Surface Area_A / Surface Area_B = (16π * r_B^2) / (4π * r_B^2) = 4.
Therefore, the ratio of the surface area of star 'A' to the surface area of star 'B' is 4.