Basic Geometric Concepts - Problems on Circles for Exams

Basic Geometric Concepts - Problems on Circles

Q. A circle has a radius of 4 m. What is the length of an arc that subtends a central angle of 90 degrees?

A. π/2 m
B. 2π m
C. 4 m
D. 3.14 m

Solution

Arc length = (θ/360) * 2πr; θ = 90; Arc length = (90/360) * 2π(4) = π/2 m.

Correct Answer: A — π/2 m

Learn More →

Q. A circle is inscribed in a square. If the side of the square is 8 cm, what is the radius of the circle?

A. 2 cm
B. 4 cm
C. 6 cm
D. 8 cm

Solution

The radius of the inscribed circle is half the side of the square, so r = 8/2 = 4 cm.

Correct Answer: B — 4 cm

Learn More →

Q. A circle is inscribed in a triangle with sides 6 cm, 8 cm, and 10 cm. What is the radius of the inscribed circle?

A. 2 cm
B. 3 cm
C. 4 cm
D. 5 cm

Solution

Semi-perimeter = (6+8+10)/2 = 12 cm; Area = √(12(12-6)(12-8)(12-10)) = 24 cm²; Radius = Area/semi-perimeter = 24/12 = 2 cm.

Correct Answer: B — 3 cm

Learn More →

Q. A circle is inscribed in a triangle with sides 8 cm, 15 cm, and 17 cm. What is the radius of the inscribed circle?

A. 4 cm
B. 5 cm
C. 6 cm
D. 7 cm

Solution

Semi-perimeter = (8 + 15 + 17)/2 = 20 cm. Area = 60 cm². Radius = Area/semi-perimeter = 60/20 = 3 cm.

Correct Answer: B — 5 cm

Learn More →

Q. If a circle has a radius of 2 m, what is the area of the circle?

A. 4π m²
B. 8π m²
C. 2π m²
D. 6π m²

Solution

Area = πr² = π(2)² = 4π m².

Correct Answer: A — 4π m²

Learn More →

Q. If a circle has a radius of 9 cm, what is the area of the circle?

A. 81π cm²
B. 72π cm²
C. 36π cm²
D. 18π cm²

Solution

Area = πr² = π(9)² = 81π cm².

Correct Answer: A — 81π cm²

Learn More →

Q. If a circle has an area of 36π cm², what is its radius?

A. 6 cm
B. 4 cm
C. 3 cm
D. 2 cm

Solution

Area = πr²; 36π = πr²; r² = 36; r = 6 cm.

Correct Answer: A — 6 cm

Learn More →

Q. If two circles have radii of 3 cm and 5 cm, what is the distance between their centers if they are externally tangent?

A. 2 cm
B. 5 cm
C. 8 cm
D. 10 cm

Solution

Distance between centers = r1 + r2 = 3 + 5 = 8 cm.

Correct Answer: C — 8 cm

Learn More →

Q. If two circles have radii of 3 cm and 6 cm, what is the ratio of their areas?

A. 1:2
B. 1:3
C. 1:4
D. 1:9

Solution

Area ratio = (r1²):(r2²) = (3²):(6²) = 9:36 = 1:4.

Correct Answer: D — 1:9

Learn More →

Q. What is the area of a sector of a circle with a radius of 10 cm and a central angle of 60 degrees?

A. 50π/3 cm²
B. 100π/3 cm²
C. 25π cm²
D. 20π cm²

Solution

Area of sector = (θ/360) * πr²; = (60/360) * π(10)² = (1/6) * 100π = 50π/3 cm².

Correct Answer: A — 50π/3 cm²

Learn More →

Q. What is the diameter of a circle with a circumference of 31.4 cm?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Circumference = πd, so d = Circumference/π = 31.4/π ≈ 10 cm.

Correct Answer: B — 10 cm

Learn More →

Q. What is the diameter of a circle with an area of 50π cm²?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Area = πr², so r² = 50, thus r = √50 ≈ 7.07 cm, diameter = 2r ≈ 10 cm.

Correct Answer: B — 10 cm

Learn More →

Q. What is the distance between the center of a circle at (2, 3) and a point on the circle at (5, 7)?

A. 5
B. 4
C. 3
D. 6

Solution

Distance = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Learn More →

Q. What is the distance between the center of a circle with radius 5 cm and a point on its circumference?

A. 0 cm
B. 5 cm
C. 10 cm
D. 2.5 cm

Solution

The distance from the center to a point on the circumference is equal to the radius, which is 5 cm.

Correct Answer: B — 5 cm

Learn More →

Q. What is the length of the diameter of a circle with a circumference of 31.4 cm?

A. 10 cm
B. 5 cm
C. 15.7 cm
D. 20 cm

Solution

Circumference = πd, so d = C/π = 31.4/π = 10 cm.

Correct Answer: A — 10 cm

Learn More →

Q. What is the length of the diameter of a circle with an area of 50π cm²?

A. 10 cm
B. 8 cm
C. 6 cm
D. 12 cm

Solution

Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2r = 2√50 = 10 cm.

Correct Answer: A — 10 cm

Learn More →

Q. What is the radius of a circle whose area is 50π cm²?

A. 5 cm
B. 10 cm
C. 7.07 cm
D. 12.56 cm

Solution

Area = πr², so r² = 50, r = √50 = 7.07 cm.

Correct Answer: C — 7.07 cm

Learn More →

Showing 1 to 17 of 17 (1 Pages)

Basic Geometric Concepts - Problems on Circles

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?