A sector of circle of radius 7.2cm which substends an angle of 300$^o$ at the centre is used to form a cone. What s the radius of the base of the cone?

Analyze the question: A sector of radius 7.2 cm and angle 300° is rolled into a cone. We need the radius of the cone's base.

Concept: When a sector is rolled into a cone:

• The sector's radius becomes the slant height of the cone (l = 7.2 cm).
• The sector's arc length becomes the circumference of the cone's base.

Solution:

Arc length of the sector = (θ/360) × 2πR = (300/360) × 2π × 7.2

This equals the base circumference, 2πr:

2πr = (300/360) × 2π × 7.2

Cancel 2π from both sides:

r = (300/360) × 7.2 r = (5/6) × 7.2 r = 6 cm

Answer: The base radius is 6 cm, which is option C.

Tip: For any sector-to-cone problem, use the shortcut r = (θ/360) × R, where R is the sector radius. Here the fraction 300/360 simplifies to 5/6, and 5/6 of 7.2 gives 6. Always check that your answer is smaller than the slant height, since the base radius must be less than l.