3.4 Arc length and sector areaIB Maths: Applications and Interpretation HL: Subtopic test

1. 1
   A sector of a circle has radius 12 cm and the angle at the centre is $75^\circ$.

   (a)

   Find the length of the arc of the sector.

   [1 mark]

   • A$94.2$ cm
   • B$15.7$ cm
   • C$31.4$ cm
   • D$7.85$ cm

   (b)

   Find the area of the sector.

   [1 mark]

   • A$15.7$ cm$^2$
   • B$47.1$ cm$^2$
   • C$94.2$ cm$^2$
   • D$452$ cm$^2$

   (c)

   Find the perimeter of the sector.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The minute hand of a clock has length 9 cm. It starts at the 12 and turns clockwise for 25 minutes.

   (a)

   Through what angle does the minute hand turn?

   [1 mark]

   • A$25^\circ$
   • B$75^\circ$
   • C$120^\circ$
   • D$150^\circ$

   (b)

   Find the distance travelled by the tip of the minute hand.

   [1 mark]

   • A$23.6$ cm
   • B$106$ cm
   • C$56.5$ cm
   • D$11.8$ cm

   (c)

   Find the area swept out by the minute hand.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A sector $OAB$ of a circle with centre $O$ has radius 8 cm. The arc $AB$ has length 14 cm.

   (a)

   Find the angle $A\hat{O}B$, and hence find the area of the sector $OAB$.

   [3 marks]

   (b)

   The chord $AB$ divides the sector into a triangle $OAB$ and a segment. Find the area of the segment.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A garden is a sector of a circle with centre $O$, radius 6 m and angle $140^\circ$. A flower bed is a sector with the same centre and the same angle, but with radius 4 m. The rest of the garden is a paved path.

   (a)

   (i) Find the length of the curved edge of the garden.
   (ii) Fencing is put along the whole boundary of the garden (the curved edge and the two straight edges) at 12 EUR per metre. Find the cost.
   (iii) Find the area of the garden.

   [6 marks]

   (b)

   (i) Find the area of the flower bed.
   (ii) Find the area of the path.
   (iii) Find the percentage of the garden that is path.

   [6 marks]

   Total for question 4: 12 marks

End of questions