Circles — Geometry and Trigonometry

Questions in this quiz (10)

1. The radius of the circle is $$9$$ units. What is the length of the diameter?

   • $$81$$
   • $$9\pi$$
   • $$18$$
   • $$81\pi$$

2. The radius of the circle is $$9$$ units. What is the circumference of the circle?

   • $$9\pi$$
   • $$18\pi$$
   • $$81\pi$$
   • $$81$$

3. The radius of a circle is $$11$$ units. What is the area of this circle?

   • $$11\pi$$
   • $$22\pi$$
   • $$22$$
   • $$121\pi$$

4. What is the measure, in radians, of the central angle that subtends $$\frac{3}{8}$$ of a circle?

   • $$\frac{3}{8}\pi$$
   • $$\frac{3}{16}\pi$$
   • $$\frac{3}{4}\pi$$
   • $$\frac{2}{3}\pi$$

5. If the central angle $$AOB$$ above is equal to $$120^{\circ}$$ and the radius is $$9$$ units, what is the length of the arc $$AB$$?

   • $$12\pi$$
   • $$9\pi$$
   • $$6\pi$$
   • $$3\pi$$

6. A circle has a central angle $$AOB$$ of $$150^{\circ}$$ and a radius of $$10$$ units. What is the area of the sector, in square units?

   • $$\frac{5}{12}\pi$$
   • $$\frac{125}{3}\pi$$
   • $$\frac{5}{6}\pi$$
   • $$\frac{5}{3}\pi$$

7. Consider a circle with the equation $$(x+3)^{2}+(y-2)^{2}=49$$. What are the coordinates of the center of the circle?

   • $$(-3,-2)$$
   • $$(3,-2)$$
   • $$(-3,2)$$
   • $$(3,2)$$

8. Consider a circle with the equation $$(x+5)^2+(y-1)^2=81$$ What is the radius of the circle?

   • $$81$$
   • $$9$$
   • $$5$$
   • $$1$$

9. What is the equation of a circle with center $$(-5,7)$$ and radius $$6$$?

   • $$(x-5)^{2}+(y+7)^{2}=36$$
   • $$(x-5)^{2}+(y-7)^{2}=6$$
   • $$(x+5)^{2}+(y-7)^{2}=36$$
   • $$(x-5)^{2}+(y+7)^{2}=6$$

10. How would you rewrite the following equation for a circle to shift it $$4$$ units upward, $$5$$ units to the left, and change the radius to $$6$$?$$(x+1)^{2}+(y-3)^{2}=16$$

    • $$(x+7)^{2}+(y+2)^{2}=36$$
    • $$(x+6)^{2}+(y-7)^{2}=36$$
    • $$(x-7)^{2}+(y+2)^{2}=16$$
    • $$(x-4)^{2}+(y+1)^{2}=36$$