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Hoshi is building a circular pond in a square section of her backyard (September 2023 - G01)

Updated on 05/21/2024

Hoshi is building a circular pond in a square section of her backyard. The square section measures 20 feet on each side. The pond touches all 4 sides of the square section. Approximately what is the total area, in square feet, of the region inside this square section but outside the circular pond?

A. 86
B. 126
C. 314
D. 337
E. 714


Solution

Correct answer: A. 86.
The area of the square section is 20 ft x 20 ft = 400 sq ft.
The diameter of the circle is the same as the side length of the square, so the diameter is 20 ft. The radius of the circle is then half the diameter, or 10 ft.
The area of the circle is pi * r^2 = pi * (10 ft)^2 = 100 pi sq ft.
We are approximating pi with 3.14, so the area of the circle is approximately 314 sq ft.

The area of the region inside the square section but outside the circular pond is then the area of the square minus the area of the circle. This is 400 sq ft - 314 sq ft = 86 sq ft.

Exam Edition: September 2023 - G01

Exam Year: 2023

Related topics: Area, Units

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