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Carts and Wheels - Introduction to Circles

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A circle is a perfectly round shape where every point on its boundary is at the same distance from a fixed point called the center.

A circle showing the center point.
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The distance from the center of the circle to any point on its edge is called the radius (rr). All radii of the same circle are equal in length.

A circle with a line segment from the center to the edge representing the radius.
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The diameter (dd) is a straight line passing through the center of the circle, connecting two points on the boundary. The diameter is exactly twice the length of the radius: d=2×rd = 2 \times r.

A circle with a line passing through the center representing the diameter.
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The boundary of a circle is called its circumference. Objects like bangles, coins, and wheels are examples of circular shapes seen in daily life.

📐Formulae

Diameter = 2×Radius2 \times \text{Radius}

Radius = Diameter2\frac{\text{Diameter}}{2}

d=2rd = 2r

r=d2r = \frac{d}{2}

💡Examples

Problem 1:

If the radius of a small cart wheel is 77 cm, find the diameter of the wheel.

Solution:

  1. Identify the given value: Radius (rr) = 77 cm.
  2. Use the formula: d=2×rd = 2 \times r.
  3. Substitute the value: d=2×7d = 2 \times 7 cm.
  4. Calculate: d=14d = 14 cm.

Explanation:

Since the diameter is always twice the length of the radius, we multiply the given radius by 22 to find the total width across the center of the wheel.

Problem 2:

A circular plate has a diameter of 2424 cm. What is the length of its radius?

Solution:

  1. Identify the given value: Diameter (dd) = 2424 cm.
  2. Use the formula: r=d2r = \frac{d}{2}.
  3. Substitute the value: r=242r = \frac{24}{2} cm.
  4. Calculate: r=12r = 12 cm.

Explanation:

The radius is exactly half of the diameter. By dividing the total width of the plate (diameter) by 22, we find the distance from the center to the edge.

Problem 3:

A rope is tied to a nail in the center of a field to draw a circle. If the length of the rope is 55 m, what is the diameter of the circle formed?

A circle with a 5m radius representing a rope tied to a nail.

Solution:

Radius (rr) = 55 m Diameter (dd) = 2×r2 \times r d=2×5d = 2 \times 5 d=10d = 10 m

Explanation:

The rope acts as the radius because it connects the center (nail) to the boundary. The diameter is double the radius, so 2×5=102 \times 5 = 10 m.

Problem 4:

Two circles are drawn inside each other. The radius of the inner circle is 44 cm and the radius of the outer circle is 99 cm. What is the distance between the boundaries of the two circles?

Two concentric circles with radii 4 cm and 9 cm.

Solution:

Outer Radius (RR) = 99 cm Inner Radius (rr) = 44 cm Distance = R−rR - r Distance = 9−49 - 4 Distance = 55 cm

Explanation:

To find the gap between the two circles, subtract the inner radius from the outer radius.