Samacheer Kalvi Class 4 Maths Solutions Term 1 Chapter 1 Geometry Exercise 1.4

Tamilnadu Samacheer Kalvi 4th Maths Solutions Term 1 Chapter 1 Geometry Ex 1.4

A. Fill in the blanks.

Question (i). All the radii of a circle are _______.
Answer: All the lines drawn from the center of a circle to any point on its edge are always the same length. This ensures the circle is perfectly round at every point.
In simple words: All radii of a circle are equal.

🎯 Exam Tip: Remember that "radii" is the plural form of "radius".

Question (ii). The _______ is the longest chord of a circle.
Answer: The longest line segment you can draw across a circle, touching two points on the edge and passing through the center, is called its diameter. It also always goes through the exact middle of the circle.
In simple words: The diameter is the longest line that goes through a circle from one side to the other.

🎯 Exam Tip: A chord is any line segment connecting two points on a circle, but the diameter is the special chord that passes through the center.

Question (iii). A line segment joining any point on the circle to its center is called _______ the of the circle.
Answer: A line drawn from the very center of a circle to any point on its outer edge is known as the radius of that circle. The radius is half the length of the diameter.
In simple words: The radius is a line from the center to the edge of a circle.

🎯 Exam Tip: Always specify "radius of the circle" to be precise.

Question (iv). A line segment with its end points on the circle is called a _______.
Answer: Any straight line that connects two different points on the outer edge of a circle is called a chord. A diameter is a special type of chord that passes through the center.
In simple words: A chord is a line that joins two points on the circle's edge.

🎯 Exam Tip: Distinguish between a chord (any two points) and a diameter (two points, through the center).

Question (v). Twice the radius is _______.
Answer: When you double the length of a circle's radius, you get its diameter. This relationship is fundamental to understanding a circle's size.
In simple words: If you multiply the radius by two, you get the diameter.

🎯 Exam Tip: Remember the simple formula: Diameter \( = 2 \times \) Radius.

B. Find the diameter of the circle.

Question (i). If the radius is \(10 \, \text{cm}\), find the diameter.
Answer: To find the diameter, we multiply the radius by 2. So, for a radius of \(10 \, \text{cm}\), the diameter will be \(2 \times 10 \, \text{cm} = 20 \, \text{cm}\). The diameter is the largest distance across the circle.
In simple words: The diameter is always twice the radius. So, 2 times 10 gives 20 cm.

🎯 Exam Tip: Always write the units (like cm) in your final answer to avoid losing marks.

Question (ii). If the radius is \(8 \, \text{cm}\), find the diameter.
Answer: We calculate the diameter by multiplying the radius by 2. For a radius of \(8 \, \text{cm}\), the diameter is \(2 \times 8 \, \text{cm} = 16 \, \text{cm}\). Understanding this helps in calculating the circumference of the circle.
In simple words: For an 8 cm radius, the diameter is 2 times 8, which is 16 cm.

🎯 Exam Tip: Clearly show the multiplication step: \(2 \times \text{radius}\).

Question (iii). If the radius is \(6 \, \text{cm}\), find the diameter.
Answer: To get the diameter, we multiply the radius by 2. Thus, for a radius of \(6 \, \text{cm}\), the diameter is \(2 \times 6 \, \text{cm} = 12 \, \text{cm}\). This formula works for all circles, no matter their size.
In simple words: If the radius is 6 cm, the diameter is 2 times 6, or 12 cm.

🎯 Exam Tip: Practice these calculations to quickly find diameters from given radii.

C. Find the radius of the circle.

Question (i). If the diameter is \(24 \, \text{cm}\), find the radius.
Answer: To find the radius, we divide the diameter by 2. So, for a diameter of \(24 \, \text{cm}\), the radius will be \( \frac{24}{2} \, \text{cm} = 12 \, \text{cm} \). The radius helps define the curve of the circle.
In simple words: The radius is half of the diameter. So, 24 divided by 2 gives 12 cm.

🎯 Exam Tip: Remember the inverse formula: Radius \( = \frac{\text{Diameter}}{2} \).

Question (ii). If the diameter is \(30 \, \text{cm}\), find the radius.
Answer: We calculate the radius by dividing the diameter by 2. For a diameter of \(30 \, \text{cm}\), the radius is \( \frac{30}{2} \, \text{cm} = 15 \, \text{cm} \). This is a fundamental concept in circle geometry.
In simple words: For a 30 cm diameter, the radius is 30 divided by 2, which is 15 cm.

🎯 Exam Tip: Always ensure your division is correct and state the units in your answer.

Question (iii). If the diameter is \(76 \, \text{cm}\), find the radius.
Answer: To get the radius, we divide the diameter by 2. Thus, for a diameter of \(76 \, \text{cm}\), the radius is \( \frac{76}{2} \, \text{cm} = 38 \, \text{cm} \). Knowing the radius is essential for drawing a circle with a compass.
In simple words: If the diameter is 76 cm, the radius is 76 divided by 2, or 38 cm.

🎯 Exam Tip: Clearly show the division step: \( \frac{\text{diameter}}{2} \).