I have really been struggling with this one and have come up with a wide variety of answers. Any help would be great:
If the radius of a planet is larger than that of Earth by a factor of 8.25, how much bigger is the surface area of the planet than Earth’s?
To calculate the surface area of a sphere, you need to know its radius. In this case, we'll compare the surface area of the planet to that of Earth.
The surface area of a sphere can be found using the formula:
Surface Area = 4πr²
Let's assume that the radius of Earth is 'r' (in some units). Since the radius of the new planet is 8.25 times larger than Earth's radius, we can express the radius of the new planet as 8.25r.
Now, we can calculate the surface area of the new planet using the given information:
Surface Area of new planet = 4π(8.25r)²
Simplifying the equation further:
Surface Area of new planet = 4π(8.25²)r²
Surface Area of new planet = 4π(68.0625)r²
Surface Area of new planet = 272.25πr²
Therefore, the surface area of the new planet is approximately 272.25 times the surface area of Earth.
This means that the surface area of the new planet is about 272.25 times bigger than Earth's surface area.