To find the circumference and area of a circle with a diameter of \( 21\pi \), you can use the following formulas: 1. **Circumference (C)**: \[ C = \pi \times d \] where \( d \) is the diameter. Substituting \( d = 21\pi \): \[ C = \pi \times (21\pi) = 21\pi^2 \] 2. **Area (A)**: \[ A = \pi r^2 \] where \( r \) is the radius. The radius is half the diameter: \[ r = \frac{d}{2} = \frac{21\pi}{2} \] Now calculate the area: \[ A = \pi \left(\frac{21\pi}{2}\right)^2 = \pi \cdot \frac{441\pi^2}{4} = \frac{441\pi^3}{4} \] So for a circle with a diameter of \( 21\pi \): - Circumference: \( 21\pi^2 \) - Area: \( \frac{441\pi^3}{4} \)

21pi diameter

1 answer

To find the circumference and area of a circle with a diameter of \( 21\pi \), you can use the following formulas:

Circumference (C): \[ C = \pi \times d \] where \( d \) is the diameter.

Substituting \( d = 21\pi \): \[ C = \pi \times (21\pi) = 21\pi^2 \]
Area (A): \[ A = \pi r^2 \] where \( r \) is the radius. The radius is half the diameter: \[ r = \frac{d}{2} = \frac{21\pi}{2} \]

Now calculate the area: \[ A = \pi \left(\frac{21\pi}{2}\right)^2 = \pi \cdot \frac{441\pi^2}{4} = \frac{441\pi^3}{4} \]

So for a circle with a diameter of \( 21\pi \):

Circumference: \( 21\pi^2 \)
Area: \( \frac{441\pi^3}{4} \)