Perimeters and areas of plane figures (circles)

Advanced Math 7 · Unit 12 · circles-arcs-sectors

circles-arcs-sectors

Name ______________________________Date ______________

1.
A circle has diameter $14$ cm. Its circumference is $k\pi$ cm. Enter $k$ .
Answer: ______________
2.
A sector of a circle has radius $9$ cm and central angle $120^\circ$ . Its area is $k\pi$ cm². Enter $k$ .
Answer: ______________
3.
A square has side $8$ cm. A quarter circle with its center at one corner of the square and radius $8$ cm is cut away. Using $\pi \approx 3.14$ , what is the area of the remaining piece, in cm²?
Answer: ______________
4.
A sector has radius $6$ cm and central angle $60^\circ$ . What is its area?
1. (A)
  $\dfrac{3}{2}\pi$ cm²
2. (B)
  $2\pi$ cm²
3. (C)
  $6\pi$ cm²
4. (D)
  $36\pi$ cm²
5.
A circle is inscribed in a square of side $12$ , touching all four sides. The total area of the four corner regions — inside the square but outside the circle — can be written as $a - b\pi$ for positive integers $a$ and $b$ . What is $a + b$ ?
1. (A)
  $108$
2. (B)
  $144$
3. (C)
  $156$
4. (D)
  $180$
5. (E)
  $288$