**1.** The area of a minor sector of a circle with a radius of 8 cm and a central angle of 45° is:

a) 42 cm^{2}b) 12 cm^{2}c) 85 cm^{2}d) 27 cm^{2}

**Answer:** b) 25.12 cm²

**Explanation:** The formula to calculate the area of a minor sector is

A = (θ/360) x π x r^{2}, where θ is the central angle and r is the radius of the circle. Substituting the given values, we get (45/360) x π x 8^{2} = (1/8) x π x 64 = 8π = 25.12 cm^{2} (approx.).

**2.** The area of a major sector of a circle with a radius of 10 cm and a central angle of 300° is:

a) 131.42 cm^{2}b) 162.83 cm^{2}c) 252.36 cm^{2}d) 261.66 cm^{2}

**Answer:** d) 261.66 cm²

**Explanation:** The formula to calculate the area of a major sector is A = (θ/360) x π x r^{2}, where θ is the central angle and r is the radius of the circle. Plugging in the values, we get (300/360) x π x 10^{2} = (5/6) x 3.14 x 100 = 261.66 cm^{2}.

**3.** The length of an arc in a circle with a radius of 30 cm and a central angle of 120° is:

a) 10π cm

b) 20π cm

c) 30π cm

d) 40π cm

**Answer:** b) 20π cm.

**Explanation:** Using the same formula as above, we have

C = (120/360) x 2π x 30 = (1/3) x 2π x 30 = 20π cm.

**4.** What is the area of the major segment of a circle with a radius of 8 cm and a central angle of 60°?

a) 181.059 cm^{2}b) 184.457 cm^{2}c)195.112 cm^{2}d) 206.458 cm^{2}

**Answer:** c) 195.112 cm^{2}

**Explanation:** The formula to calculate the area of the major segment is (θ_{1}/360) x π x r^{2} + (1/2) x r^{2} x sin(θ_{2}), where θ_{1} is the angle of the major sector and θ_{2} is the central angle of the triangle and r is the radius of the circle. So, θ_{1} = 300°, θ_{2} = 60° and r = 8 cm. Plugging in the values, we get (300/360) x π x 8^{2} + (1/2) x 8^{2} x sin (60°) = (5/6) x π x 64 + (1/2) x 64 x (√3/2) = 195.112 cm^{2}.

**5.** What is the area of a ring in a circle with an outer radius of 10 cm and an inner radius of 6 cm?

a) 12π cm^{2}b) 36π cm^{2}c) 50π cm^{2}d) 64π cm^{2}

**Answer:** d) 64 cm²

**Explanation:** The formula to calculate the area of a ring is π (R^{2} - r^{2}), where R is the outer radius and r is the inner radius. Plugging in the values, we get π x (10^{2} - 6^{2}) = π x (100 - 36) = π x 64 = 64π cm^{2}.

**1.** The length of an arc in a circle is 15π cm. If the central angle of the arc is 60°, what is the radius of the circle?

a) 45 cm

b) 46 cm

c) 47 cm

d) 48 cm

**Answer:** a) 45 cm

**2.** The area of a ring in a circle is 33π cm^{2}. If the inner radius is 4 cm, what is the outer radius of the ring?

a) 6 cm

b) 7 cm

c) 10 cm

d) 12 cm

**Answer:** b) 7 cm

**3.** The central angle of an arc is 90°. If the length of the arc is 12π cm, what is the radius of the circle?

a) 13 cm

b) 18 cm

c) 21 cm

d) 24 cm

**Answer:** d) 24 cm

**4.** The length of an arc in a circle is 24π cm. If the radius of the circle is 18 cm, what is the central angle of the arc?

a) 60°

b) 190°

c) 240°

d) 310°

**Answer:** c) 240°

**5.** The area of a minor sector of a circle is 54π cm^{2}. If the central angle of the sector is 60°, what is the radius of the circle?

a) 23 cm

b) 18 cm

c) 16 cm

d) 12 cm

**Answer:** b) 18 cm

**6.** The area of a circle is 154π cm^{2}. What is the radius of the circle approximately?

a) 7 cm

b) 10 cm

c) 11 cm

d) 13 cm

**Answer:** d) 13 cm

**7.** The circumference of a circle is 30π cm. What is the radius of the circle?

a) 5 cm

b) 10 cm

c) 15 cm

d) 20 cm

**Answer:** c) 15 cm.

**8.** What is the area of a ring with an outer radius of 13 cm and an inner radius of 12 cm?

a) 196π cm^{2}b) 207π cm^{2}c) 305π cm^{2}d) 344π cm^{2}

**Answer:** b) 207π cm^{2}

**9.** What is the area of the triangle formed by a sector of a circle with a central angle of 45° and a radius of 6 cm?

a) 9 cm^{2}b) 12 cm^{2}c) 18 cm^{2}d) 24 cm^{2}

**Answer:** c) 18 cm^{2}

**10.** The central angle of a sector in a circle is 60°. If the area of the triangle formed by the sector is 12 cm^{2}, what is the radius of the circle?

a) 2 cm

b) 3 cm

c) 4 cm

d) 6 cm

**Answer:** a) 2 cm

>> Join CREST Olympiads WhatsApp Channel for latest updates.