A cone was developed from a sector of a circle with radius10cm and an angle at the centre of 108°. What is the radius of the cone?

Analyze the question: A sector of a circle (radius 10 cm, angle 108°) is rolled into a cone. We need the radius of the cone's base.

Concept:

• The radius of the sector becomes the slant height (l) of the cone.
• The arc length of the sector becomes the circumference of the cone's base.

Solution:

Arc length of the sector = (θ/360) × 2πR = (108/360) × 2π × 10 = 0.3 × 20π = 6π cm

This equals the circumference of the base of the cone: 2πr = 6π r = 3 cm

Check using the shortcut: r = (θ/360) × l = (108/360) × 10 = 3 cm ✔

Answer: The radius of the cone is 3.0 cm, which is option E.

Tip: For a cone made from a sector, always use r = (θ/360) × l, where l is the sector's radius. It saves time in the exam, so remember "sector radius = slant height, arc = base circumference."