The area of the circle = π r² = π (d/2)² Where r is the radius of the circle And d is the diameter of the circle d = 2r OR r = d/2 given d = 10 in ∴ r = d/2 = 10/2 = 5 in ∴ The area of the circle = π r² = π * 5² = 25π ≈ 78.54 in²
The correct answer is the fourth option 78.54
========================================== very important note: There is a mistake in the dimension of the answers. The dimension of the given diameter is inch , while the dimensions of the answers is square cm. If it is required to find the area in square cm ∵ 1 inch = 2.54 cm ∴ r = d/2 = 10/2 = 5 in = 5 * 2.54 cm = 12.7 cm
∴ Area = π r² = π * (12.7)² = 161.29π ≈ 506.7 square cm
What is the area of a circle with a diameter measuring 10 inches? 31.4 square cm 81.41 square cm 153.93 square cm 78.54 square cm
In solving this problem, let us recall the formula for the area of a circle: We know that the formula for the area of a circle is given by: A= (pi)(r^2)
Since in this problem, the diameter is given by 10 inches: But diameter= radius(r) times 2 D= 2r Thus; r=5 inches
Substitute: A= (pi)(5^2) A=78.54 square inches
Convert inches to cm since the choices are in cm: 1 inch= 2.54 cm
78.54 inches(2.54 cm/1 inch) A=199.49 square cm
Since the correct answer is not in the given choices, it can be assumed that the choices have a wrong label/unit. We can then say that the correct answer should be: A=78.54 square inches or A=199.49 square cm
