Final answer:
To find the surface area of the larger ball, square the ratio of the diameters (1:1.2) to get the ratio of the surface areas as 1:1.44. Multiply the surface area of the smaller ball (200 cm²) by 1.44 to arrive at a surface area of 288 cm² for the larger ball.
Step-by-step explanation:
To find the surface area of the larger ball, we can use the ratio of the diameters and the surface area of the smaller ball provided. The ratio of the diameters is given as 1:1.2. The surface area of a sphere is calculated using the formula A = 4πr², where A is the surface area and r is the radius. Because the radius is half of the diameter, if the diameter increases by a factor of 1.2, the radius also increases by a factor of 1.2.
If the surface area of the smaller ball is 200 cm² (due to surface area to volume ratio increasing with a decrease in the size of the ball), we need to square the ratio of the diameters to find the ratio of surface areas. This gives us (1²):(1.2²) = 1:1.44. Now we can find the surface area of the larger ball by multiplying the area of the smaller one by 1.44:
Surface Area of Larger Ball = 200 cm² × 1.44 = 288 cm².
Therefore, the surface area of the larger ball is 288 cm².