Worksheets · Foundation and Higher

Arc lengths and sectors

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Calculator · 3 marks

   A round pizza has a diameter of 30 cm. It is cut into 8 equal slices from the centre.

   (a) Work out the area of one slice. Give your answer correct to 3 significant figures. (3)
2. Question 2Non-calculator · 4 marks

   A sector has angle $45^\circ$ and area $8\pi$ cm².

   (a) Find the radius of the sector. (2)

   (b) Find the exact arc length of the sector. (2)
3. Question 3Non-calculator · 6 marks

   A sector $OAB$ of a circle has radius 6 cm. The area of the sector is $15\pi\text{ cm}^2$.

   (a) Work out the angle $AOB$. (2)

   (b) Work out the perimeter of the sector. Give your answer in the form $a + b\pi$. (2)

   (c) The sector is folded so that $OA$ meets $OB$, making a cone with no base. Work out the radius of the base of the cone. (2)