Answer:
Therefore, when the radius of a sphere is increased by 25%, the surface area increases by approximately 56.25%.
Step-by-step explanation:
The surface area of a sphere is given by the formula: Surface Area = 4πr^2 where r is the radius of the sphere.
To find the percentage increase in surface area when the radius is increased by 25%, we can follow these steps:
1. Let's assume the initial radius of the sphere is r.
2. If the radius is increased by 25%, the new radius will be 1.25r (since 25% is equivalent to multiplying by 1.25).
3. Now, we can calculate the initial surface area (A1) using the formula: A1 = 4πr^2. 4.
Similarly, we can calculate the new surface area (A2) using the formula: A2 = 4π(1.25r)^2 = 4π(1.5625r^2) = 6.25πr^2.
5. The percentage increase in surface area can be calculated as follows: Percentage Increase = ((A2 - A1) / A1) * 100
6. Plugging in the values we obtained earlier,
we have: Percentage Increase = ((6.25πr^2 - 4πr^2) / 4πr^2) * 100 = ((2.25πr^2) / 4πr^2) * 100 = 56.25%