Areas Related to Circles — Practice

Question 1

Find the circumference of a circle of radius 7 cm (π = 22/7).

Accepted Answer

Step 1 — 2πr = 2 × 22/7 × 7 = 44 cm.

✦ Answer: 44 cm.

Question 2

Find the area of a circle of radius 14 cm (π = 22/7).

Accepted Answer

Step 1 — πr² = 22/7 × 14 × 14 = 22 × 28 = 616 cm².

✦ Answer: 616 cm².

Question 3

Find the length of a 90° arc of a circle of radius 14 cm (π = 22/7).

Accepted Answer

Step 1 — (90/360) × 2 × 22/7 × 14 = (1/4) × 88 = 22 cm.

✦ Answer: 22 cm.

Question 4

Find the area of a sector of radius 21 cm with central angle 60° (π = 22/7).

Accepted Answer

Step 1 — (60/360) × 22/7 × 21² = (1/6) × 22/7 × 441.

Step 2 — = (1/6) × 1386 = 231 cm².

✦ Answer: 231 cm².

Question 5

Find the area swept by the minute hand of length 14 cm in 15 minutes (π = 22/7).

Accepted Answer

Step 1 — In 15 min the minute hand turns 15 × 6° = 90°.

Step 2 — Sector area = (90/360) × 22/7 × 14² = (1/4) × 616 = 154 cm².

✦ Answer: 154 cm².

Question 6

Find the area of the minor segment of a circle of radius 10 cm cut off by a chord subtending 90° at the centre (π = 3.14).

Accepted Answer

Step 1 — Sector = (90/360) × 3.14 × 100 = 78.5 cm².

Step 2 — Triangle = ½ × r² × sin90° = ½ × 100 × 1 = 50 cm².

Step 3 — Segment = 78.5 − 50 = 28.5 cm².

✦ Answer: 28.5 cm².

Question 7

The radii of two circles are 8 cm and 6 cm. Find the radius of the circle whose area equals the sum of their areas.

Accepted Answer

Step 1 — πR² = π(8²) + π(6²) ⇒ R² = 64 + 36 = 100.

Step 2 — R = 10 cm.

✦ Answer: 10 cm.

Question 8

A square of side 14 cm has a circle inscribed in it. Find the area between the square and the circle (π = 22/7).

Accepted Answer

Step 1 — Circle radius = 7 cm; circle area = 22/7 × 49 = 154 cm².

Step 2 — Square area = 14² = 196 cm².

Step 3 — Shaded = 196 − 154 = 42 cm².

✦ Answer: 42 cm².

Question 9

From each corner of a square of side 14 cm, a quadrant of radius 7 cm is cut off, and a circle of diameter 7 cm is removed from the centre. Find the remaining area (π = 22/7).

Accepted Answer

Step 1 — Square = 196 cm². Four quadrants = one full circle radius 7 = 154 cm².

Step 2 — Central circle: radius 3.5, area = 22/7 × 3.5² = 38.5 cm².

Step 3 — Remaining = 196 − 154 − 38.5 = 3.5 cm².

✦ Answer: 3.5 cm².

Question 10

Find the area of the minor segment of a circle of radius 21 cm cut by a chord subtending 60° at the centre (π = 22/7, √3 ≈ 1.73).

Accepted Answer

Step 1 — Sector = (60/360) × 22/7 × 441 = 231 cm².

Step 2 — Triangle = ½ × 21² × sin60° = ½ × 441 × (√3/2) ≈ 190.6 cm².

Step 3 — Segment ≈ 231 − 190.6 = 40.4 cm².

✦ Answer: ≈ 40.4 cm².

Practice — Areas Related to Circles

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