If the diameter of a circle is 10 units, what is its area?

If the diameter of a circle is 10 units, what is its area?

• A. 20π square units
• B. 25π square units
• C. 30π square units
• D. 15π square units

Answer: (B)

To determine the area of a circle, we use the formula: \[ \text{Area} = \pi r^2 \] where \( r \) is the radius of the circle. Given that the diameter of the circle is 10 units, we first need to find the radius. The radius is half of the diameter: \[ r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \text{ units} \] Now we can substitute the radius back into the area formula: \[ \text{Area} = \pi (5)^2 = \pi \times 25 = 25\pi \text{ square units} \] Thus, the area of the circle is indeed \( 25\pi \) square units, confirming that the answer is correct. This calculation accurately reflects the relationship between the diameter and the radius and applies the area formula for a circle correctly.

To determine the area of a circle, we use the formula:

[

\text{Area} = \pi r^2

]

where ( r ) is the radius of the circle. Given that the diameter of the circle is 10 units, we first need to find the radius. The radius is half of the diameter:

[

r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5 \text{ units}

]

Now we can substitute the radius back into the area formula:

[

\text{Area} = \pi (5)^2 = \pi \times 25 = 25\pi \text{ square units}

]

Thus, the area of the circle is indeed ( 25\pi ) square units, confirming that the answer is correct. This calculation accurately reflects the relationship between the diameter and the radius and applies the area formula for a circle correctly.