Neokaal Study
Areas Related to Circles
Competency Practice
Sector and segment areas, clock sweeps, wiper sweeping regions, and tethered field problems.
- Name
- Class
- Date
Answer all questions.
Show all necessary working.
Use a separate notebook for your solutions.
An arc in a circle of radius 6 cm subtends $60^\circ$ at the centre. Find its length, sector area, and minor-segment area.
A chord subtends $90^\circ$ at the centre of a circle of radius 6 cm. Find the minor segment area.
A clock's minute hand is 21 cm long. Find the area it sweeps in 5 minutes.
Two non-overlapping wipers, each 28 cm long, sweep through $130^\circ$. Find their total cleaned area.
A grazing rope of length 13 m is tied at a corner of a square field of side 16 m. Find the accessible area.
A chord subtends $120^\circ$ at the centre of a circle of radius 15 cm. Find the corresponding minor segment area.
Neokaal Study
Answer Key
arc $=6\pi/3$ cm; sector $=36\pi/6$ cm$^2$; segment $=36\pi/6-36\sqrt3/4$ cm$^2$
- Identify the central angle as a fraction of $360^\circ$.
- Apply the arc or sector formula and simplify.
$\frac{36}4\pi-\frac{36}2$ cm$^2$
- Segment area equals sector area minus the area of the triangle formed by the radii.
- Use the complementary part of the circle when a major region is requested.
$\frac{147\pi}{4}$ cm$^2$
- Identify the central angle as a fraction of $360^\circ$.
- Apply the arc or sector formula and simplify.
$\frac{5096\pi}{9}$ cm$^2$
- Identify the central angle as a fraction of $360^\circ$.
- Apply the arc or sector formula and simplify.
$\frac{169}4\pi$ m$^2$
- Identify the central angle as a fraction of $360^\circ$.
- Apply the arc or sector formula and simplify.
$\frac{225}3\pi-\frac{225}4\sqrt3$ cm$^2$
- Segment area equals sector area minus the area of the triangle formed by the radii.
- Use the complementary part of the circle when a major region is requested.