Final answer:
When the radius of a circular plate is tripled, the new area is 5625π square inches.
Step-by-step explanation:
To find the new area of the circular plate when the radius is tripled, we can use the formula for the area of a circle, which is A = πr². If the original area is 625π square inches, we can solve for the radius by rearranging the formula: r = √(A/π). Plugging in the original area, we get r = √(625π/π) = √625 = 25 inches.
When the radius is tripled, the new radius is 3 * 25 = 75 inches. Now we can find the new area by plugging this value back into the formula for the area of a circle: A = π(75)² = 5625π square inches. Therefore, the new area is 5625π square inches.