Answer :
Final answer:
The surface area of a sphere with a mass of 2 kg will be 256 cm², thus the correct option is A.
Explanation:
The surface area of a sphere is calculated using the formula A = 4πr², where A is the surface area and r is the radius of the sphere. In this case, we know that the mass of the sphere is directly proportional to its radius, and since the mass has doubled from 1 kg to 2 kg, the radius will also double. Therefore, the new radius of the sphere will be √2 times the original radius.
Now, let's consider the surface area of the sphere with a mass of 1 kg. We know that the surface area is 64 cm², so we can write the equation as 64 = 4πr². Solving for r, we get a radius of approximately 2.53 cm. Doubling this radius (√2 x 2.53 = 3.58 cm) and plugging it back into the formula, we get the new surface area as A = 4π(3.58)² = 256 cm². Therefore, the correct answer is option A) 256 cm².
In conclusion, as the mass of the sphere increases, its radius and surface area also increase in proportion. We can use the formula A = 4πr² to calculate the surface area of the sphere, and in this case, doubling the mass results in a fourfold increase in the surface area. This concept can be extended to any mass and surface area values, as long as the ratio between the two remains constant, thus the correct option is A.
