Final answer:
To find the radius of a sphere given its surface area, the formula S = 4πr^2 can be used. In this case, the surface area is 154 cm², resulting in a radius of approximately 3.51 cm. The ratio of the surface areas of two spheres can be found by squaring the ratio of their radii. With the moon's diameter being one fourth of the earth's diameter, the ratio of their surface areas is 16:1.
Step-by-step explanation:
To find the radius of a sphere whose surface area is given, use the formula:
S = 4πr^2
In this case, the surface area is 154 cm².
Plugging in the values to the formula:
154 = 4πr^2
Dividing both sides by 4π:
r^2 = 154 / (4π)
r^2 ≈ 12.33
Taking the square root of both sides:
r ≈ √(12.33)
r ≈ 3.51
Therefore, the radius of the sphere is approximately 3.51 cm.
For the second question, the ratio of the surface areas of two spheres is equal to the square of the ratio of their radii.
Given that the diameter of the moon is one fourth of the diameter of the earth, the ratio of the radii would be 1:4.
Applying the formula:
Ratio of surface areas = (4/1)^2 = 16
Therefore, the ratio of their surface areas is 16:1.
Learn more about Finding the radius and surface area of a sphere