Question 1 of 10 2 Points What is the approximate area of the circle shown below? A. 616 cm
B. 154 cm
C. 22 cm
D. 44 cm
14 cm C
The Correct Answer and Explanation is:
To find the area of the circle, we use the formula:A=πr2A = \pi r^2A=πr2
From the image, the diameter of the circle is given as 14 cm, which means the radius (r) is half of the diameter:r=142=7 cmr = \frac{14}{2} = 7 \text{ cm}r=214=7 cm
Now plug the radius into the area formula:A=π×72=π×49≈3.14×49A = \pi \times 7^2 = \pi \times 49 \approx 3.14 \times 49A=π×72=π×49≈3.14×49A≈153.86 cm2A \approx 153.86 \text{ cm}^2A≈153.86 cm2
Rounded to the nearest whole number:A≈154 cm2A \approx 154 \text{ cm}^2A≈154 cm2
✅ Correct Answer: B. 154 cm²
Explanation
The problem asks for the approximate area of a circle with a diameter of 14 cm. To find the area, we must first understand that the area of a circle depends on its radius, not the diameter. The radius is half the diameter, so in this case, the radius is:Radius=142=7 cm\text{Radius} = \frac{14}{2} = 7 \text{ cm}Radius=214=7 cm
Next, we apply the standard formula for the area of a circle:A=πr2A = \pi r^2A=πr2
Substituting the radius into the formula gives:A=π×72=π×49A = \pi \times 7^2 = \pi \times 49A=π×72=π×49
Since the problem asks for an approximate area, we use the approximation π≈3.14\pi \approx 3.14π≈3.14:A≈3.14×49=153.86 cm2A \approx 3.14 \times 49 = 153.86 \text{ cm}^2A≈3.14×49=153.86 cm2
This value is approximately 154 cm², which matches option B. The other options are either too small or too large to be correct based on the formula.
Understanding the relationship between the diameter, radius, and area of a circle is crucial in solving such problems. A common mistake is using the diameter directly in the area formula, which would result in an incorrect answer. Always remember that the radius is the key quantity for calculating the area of a circle.
