Circumference and Area of a Circle and a Sector

The formula for the circumference of a circle is $C=2\pi r$. Since the radius is 4 cm, the circumference is $2\pi \times 4=8\pi$ cm.

The formula for the circumference of a circle is $C=\pi d$. Since the diameter is 8 cm, substituting into the formula gives $C=\pi \times 8=8\pi$ cm.

The formula for the area of a circle is $A=\pi r^2$. Since the radius is 6 cm, the area is $A=\pi \times 6^2=36\pi$ cm${}^2$.

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 formula gives $A=\pi \times 5^2=25\pi$ cm${}^2$.

The formula for the area of a sector is $A=\frac{\theta }{360}\times \pi r^2$, where $\theta$ is the central angle. Here, $\theta =90^{\circ }$ and $r=8$ cm. So, $A=\frac{90}{360}\times \pi \times 8^2=\frac{1}{4}\times 64\pi =16\pi$ cm${}^2$.

The formula for the arc length of a sector is $L=\frac{\theta }{360}\times 2\pi r$, where $\theta$ is the central angle. Here, $\theta =60^{\circ }$ and $r=6$ cm. So, $L=\frac{60}{360}\times 2\pi \times 6=\frac{1}{6}\times 12\pi =2\pi$ cm.