Circumference and Area of a Circle and a Sector

Feedback: Not quite! The formula for the circumference of a circle is $C = 2\pi r$. Since the radius is 4 cm, the circumference is $2\pi \times 4 = 8\pi \, \text{cm}$.

Feedback: Not quite! The formula for the circumference of a circle is $C = \pi d$. Since the diameter is 8 cm, substituting into the formula gives $C = \pi \times 8 = 8\pi \, \text{cm}$.

Feedback: Not quite! The formula for the area of a circle is $A = \pi r^2$. Since the radius is 6 cm, the area is $A = \pi \times 6^2 = 36\pi \, \text{cm}^2$.

Feedback: Not quite! The formula for the area of a circle is $A = \pi r^2$. Since the diameter is 10 cm, the radius is $\frac{10}{2} = 5$ cm. Substituting into the area formula gives $A = \pi \times 5^2 = 25\pi \, \text{cm}^2$.

Feedback: Not quite! The formula for the area of a sector is $A = \frac{\theta}{360} \times \pi r^2$, where $\theta$ is the central angle and $r$ is the radius. In this case, $\theta = 90^\circ$ and $r = 8 \, \text{cm}$. Now, calculate the area of the sector: $A = \frac{90}{360} \times \pi \times 8^2 = \frac{1}{4} \times 64\pi = 16\pi \, \text{cm}^2$.

Feedback: Not quite! The formula for the arc length of a sector is $L = \frac{\theta}{360} \times 2\pi r$, where $\theta$ is the central angle and $r$ is the radius. In this case, $\theta = 60^\circ$ and $r = 6 , \text{cm}$. Now, calculate the arc length of the sector: $L = \frac{60}{360} \times 2\pi \times 6 = \frac{1}{6} \times 12\pi = 2\pi \, \text{cm}$.