Worksheet Solutions: Circles | Mathematics for Class 5 PDF Download

Q1: Fill in the blanks:
(i) A diameter of a circle is a chord that ______ through the centre.
(ii) A radius of a circle is a line segment with one end point ______ and the other end ______.
(iii) If we join any two points on a circle by a line segment. We obtain a ______ of the circle.
(iv) Any part of a circle is called an ______ of the circle.
Ans: (i) passes
(ii) at the centre, on the circle
(iii) chord
(iv) arc

Q2: Find the diameter of the circle whose radius is:
(i) 4 cm
(ii) 18 cm
(iii) 12 cm
(iv) 7 cm
(v) 3 cm
Ans: The formula for the diameter of a circle is: Diameter = 2 × Radius 
(i) Radius = 4cm: 2 × 4 = 8cm
(ii) Radius = 18cm: 2 × 18 = 36cm
(iii) Radius = 12cm: 2 × 12 = 24cm
(iv) Radius = 7cm: 2 × 7 = 14cm
(v) Radius = 3cm: 2 × 3 = 6cm

Q3: Find the area of the circle which circumscribes a square of side 15 units.
Ans: Diagonal of the square: The diagonal of a square circumscribes the circle, meaning it becomes the diameter of the circle.
The formula for the diagonal of a square is:

Substitute Side length = 15 Side length=15:

Radius of the circle: The radius is half the diagonal:

Area of the circle: The formula for the area of a circle is:
Area = π × Radius².
Substitute Radius = 7.5√2:

Approximation: Using π ≈ 3.1416: 
Area ≈ 225 × 3.1416 ≈ 706.86square units.
The area of the circle is approximately 706.86 square units.

Q6: A circular walking track of 3 feet width has an inner radius of 10 feet. Find the area of the circular track.
Ans: The area of the circular track is the difference between the areas of the outer and inner circles.
Outer radius: Inner radius + Width = 10 + 3 = 13 feet
Area of the outer circle: π × (Outer radius)2 = π × 132 = 169π
Area of the inner circle: π × (Inner radius)2 = π × 102 = 100π
Area of the track: Outer area − Inner area = 169π − 100π = 69π
Using π ≈ 3.1416: Area of the track ≈ 69 × 3.1416 ≈ 216.99 square feet
Approximately 216.99 square feet.

Q7: A circular wheel of 1.5 feet radius makes 1200 rotations. Find the distance covered by the circular wheel.
Ans: The distance covered by the wheel is the product of the number of rotations and the circumference of the wheel.
Circumference of the wheel: 2π × Radius = 2π × 1.5 = 3π feet
Distance covered: Number of rotations × Circumference = 1200 × 3π = 3600π
Using π ≈ 3.1416: Distance covered ≈ 3600 × 3.1416 ≈ 11,309.73 feet
Approximately 11,309.73 feet.

Q8: The circumference of a circle having a diameter of 18 units is _________.
Ans: The formula for the circumference of a circle is:
Circumference = π × Diameter
Substitute Diameter = 18: Circumference = π × 18 = 18π
Using π ≈ 3.1416: Circumference ≈ 18 × 3.1416 ≈ 56.55 units
Approximately 56.55 units.

Q9: What is the radius of a circle drawn in a square of area 121 square units?
Ans: The circle is inscribed in the square, so its diameter is equal to the side length of the square.
Side length of the square: Side length = √Area = √121 = 11 units
Radius of the circle: Radius = Diameter ÷ 2 = 11 ÷ 2 = 5.5 units
5.5 units.

Q10: A circular wheel of 1.2 feet radius makes 800 rotations. Find the distance covered by the circular wheel.
Ans: The distance covered by the wheel is the product of the number of rotations and the circumference of the wheel.
Circumference of the wheel: 2π × Radius = 2π × 1.2 = 2.4π feet
Distance covered: Number of rotations × Circumference = 800 × 2.4π = 1920π
Using π ≈ 3.1416: Distance covered ≈ 1920 × 3.1416 ≈ 6,031.85 feet
Approximately 6,031.85 feet.