What is the area of a circle with a diameter of 10 cm?

• A. 31.42 cm²
• B. 78.54 cm²
• C. 50.24 cm²
• D. 100.00 cm²

Answer: (B)

To find the area of a circle, you can use the formula:

[ \text{Area} = \pi r^2 ]

where ( r ) is the radius of the circle. Since the question provides the diameter of the circle as 10 cm, you need to first calculate the radius. The radius is half of the diameter, so:

[ r = \frac{\text{diameter}}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm} ]

Next, you can substitute the radius into the area formula:

[ \text{Area} = \pi (5 \text{ cm})^2 ]

This simplifies to:

[ \text{Area} = \pi \times 25 \text{ cm}^2 ]

Using a common approximation for ( \pi ), which is about 3.14, you can calculate the area as follows:

[ \text{Area} \approx 3.14 \times 25 \text{ cm}^2 = 78.5 \text{ cm}^2 ]

When rounding to two decimal places, you find:

[ \text{Area} \approx 78