Moderate Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Find the circumference of a circle with radius 14 cm.

Correct! Circumference = 2πr = 2 × 227 × 14 = 88 cm.

(2) Find the area of a circle with diameter 16 cm.

Perfect! Radius = 8 cm. Area = πr2 = 227 × 64 ≈ 201.06 cm2.

(3) Find the radius of a circle whose area is 154 cm2 (use π = 227).

Excellent! Area = πr2 = 154, so r2 = 154 × 722 = 49, therefore r = 7 cm.

(4) Find the circumference of a circle whose area is 154 cm2 (use π = 227).

Great! First find radius = 7 cm, then circumference = 2πr = 44 cm.

(5) Define chord and arc of a circle.

Chord is the joining points on circle while Arc is part of the .

Correct! A chord is a line segment joining two points on the circle. An arc is a part of the circumference.

Short Answer Questions (2 Marks Each)

Answer each question with detailed calculations

(1) A circular pond has diameter 21 m. Find its circumference and area (use π = 227).

Circumference: m Area: m2

Excellent! Circumference = πd = 227 × 21 = 66 m, Area = πr2 = 227 × 110.25 = 346.5 m2.

(2) A circular plate has radius 10 cm. Find its area and circumference.

Area: cm2 Circumference: cm

Perfect! Area = πr2 = 227 × 100 ≈ 314 cm2, Circumference = 2πr = 2 × 227 × 10 ≈ 62.8 cm.

(3) Find the area of a circle whose circumference is 44 cm (use π = 227).

Correct! Circumference = 2πr = 44, so r = 7 cm. Area = πr2 = 227 × 49 = 154 cm2.

(4) A circular ring has outer radius 12 cm and inner radius 7 cm. Find its area.

Great! Area = πR2−r2 = 227144−49 = 227 × 95 = 269.5 cm2.

(5) Find the radius of a circle whose circumference is 31.4 cm (use π = 3.14).

Perfect! Circumference = 2πr = 31.4, so r = 31.42×3.14 = 5 cm.

Long Answer Questions (4 Marks Each)

(1) A circular garden has radius 21 m. A path 3 m wide is made around it. Find the area of the path (using π = 227).

Area of path: m2

Correct! Garden area = π × 212 = 1386 m2. Total area with path = π × 242 = 1809.55 m2. Path area = 1809.55 - 1386 = 423.55 m2 ≈ 396 m2 .

(2) A circular wheel makes 500 revolutions and the diameter of the wheel is 84 cm. Find the distance covered by the wheel.

Distance covered: cm

Perfect! Circumference = πd = 227 × 84 = 264 cm. Distance = 500 × 264 = 132,000 cm = 1320 m.

(3) A circular pond has diameter 28 m. A path of width 4 m surrounds it. Find the area of the path.

Area of path: m2

Excellent! Pond area = π × 142 = 616 m2. Total area = π × 182 = 1017.36 m2. Path area = 1017.36 - 616 = 401.36 m2.

(4) A circular plate has radius 14 cm. A smaller circle of radius 7 cm is drawn inside it. Find the area of the ring formed.

Area of ring: cm2

Great! Area = πR2−r2 = 227196−49 = 227 × 147 = 462 cm2.

(5) A circular field has radius 35 m. A wire is to be placed along the boundary. Find the length of wire needed (use π = 227).

Length of wire: m

Correct! Length = Circumference = 2πr = 2 × 227 × 35 = 220 m.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The circumference of a circle with radius 14 cm is:

(a) 88 cm (b) 84 cm (c) 80 cm (d) 90 cm

Correct! Circumference = 2πr = 2 × 227 × 14 = 88 cm.

(2) The area of a circle with diameter 16 cm is:

(a) 201.06 cm2 (b) 200 cm2 (c) 202 cm2 (d) 199 cm2

Correct! Radius = 8 cm. Area = πr2 = 227 × 64 ≈ 201.06 cm2.

(3) The radius of a circle whose area is 154 cm2 is:

(a) 7 cm (b) 6 cm (c) 8 cm (d) 9 cm

Correct! Area = πr2 = 154, so r2 = 49, therefore r = 7 cm.

(4) The circumference of a circle with area 154 cm2 (π = 227) is:

(a) 44 cm (b) 42 cm (c) 40 cm (d) 46 cm

Correct! First find r = 7 cm, then circumference = 2πr = 44 cm.

(5) The area of a circular ring with outer radius 10 cm and inner radius 6 cm is:

(a) 214 cm2 (b) 200 cm2 (c) 210 cm2 (d) 220 cm2

Correct! Area = πR2−r2 = 227100−36 = 227 × 64 ≈ 201.14 cm2.

(6) A circle has radius 21 m. Find its circumference (use π = 227).

(a) 132 m (b) 138 m (c) 140 m (d) 144 m

Correct! Circumference = 2πr = 2 × 227 × 21 = 132 m.

(7) The area of a circle with radius 10 cm is:

(a) 314 cm2 (b) 300 cm2 (c) 320 cm2 (d) 310 cm2

Correct! Area = πr2 = 227 × 100 ≈ 314 cm2.

(8) The radius of a circle whose circumference is 31.4 cm (π = 3.14) is:

(a) 5 cm (b) 6 cm (c) 7 cm (d) 4 cm

Correct! Radius = Circumference ÷ 2π = 31.4 ÷ (2 × 3.14) = 5 cm.

(9) The area of a circle with radius 7 cm is:

(a) 154 cm2 (b) 150 cm2 (c) 160 cm2 (d) 148 cm2

Correct! Area = πr2 = 227 × 49 = 154 cm2.

(10) A circular field has radius 35 m. The length of wire needed to surround it (π = 227) is:

(a) 220 m (b) 210 m (c) 200 m (d) 230 m

Correct! Length = Circumference = 2πr = 2 × 227 × 35 = 220 m.

Advanced Circle Challenge

Determine whether these statements are True or False:

Advanced Circle Quiz