Question

A park has a large fish pond and a small fish pond, as shown.

Large fish pond
Small fish pond
Each pond is in the shape of a circle.
The radius of the large fish pond is 4 times the radius of the small fish pond.
Based on this information, which of the following statements is TRUE?
O A. The area of the large pond is 2 times the area of the small pond.
B. The area of the large pond is 4 times the area of the small pond.
C. The area of the large pond is 8 times the area of the small pond.
D. The area of the large pond is 16 times the area of the small pond.

Answer 1

Correct option is D). The area of the large pond is 16 times the area of the small pond, since the radius of the large pond is 4 times the radius of the small pond, and the area of a circle increases with the square of the radius.

Step-by-step explanation:

The student is asked to determine the relationship between the areas of two circular fish ponds given that the radius of the large fish pond is 4 times the radius of the small fish pond. To find the area of a circle, we use the formula πr², where r is the radius of the circle. If we let the radius of the small pond be r, then the radius of the large pond is 4r.

The area of the small pond is πr². The area of the large pond is π(4r)² = π(16r²) = 16πr². This shows that the area of the large pond is 16 times the area of the small pond.

Therefore, the correct statement is D. The area of the large pond is 16 times the area of the small pond.