Maharashtra Board Class 5 Maths Chapter 7 Circles Set 28 Solutions

Question 1. Draw circles with the radii given below.
(1) 2 cm
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त जिसका केंद्र 'O' है और 'OA' उसकी त्रिज्या है जिसकी लम्बाई 2 सेमी है।
In simple words: This question asks to draw circles given their radii. For 2 cm radius, draw a circle with the compass set to 2 cm.

🎯 Exam Tip: Use a compass and ruler accurately to draw circles with precise radii for full marks.

(2) 4 cm
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त जिसका केंद्र 'O' है और 'OC' उसकी त्रिज्या है जिसकी लम्बाई 4 सेमी है।
In simple words: To draw a 4 cm radius circle, open your compass to 4 cm and draw the circle.

🎯 Exam Tip: Ensure the compass point is stable and the pencil draws a continuous, smooth curve.

(3) 3 cm
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त जिसका केंद्र 'O' है और 'OB' उसकी त्रिज्या है जिसकी लम्बाई 3 सेमी है।
In simple words: For a 3 cm radius, set your compass opening to 3 cm and draw the circle.

🎯 Exam Tip: Practice drawing circles of various radii to improve accuracy and speed.

Question 2. Draw a circle of any radius. Show one diameter, one radius and one chord on that circle.
Answer: In a circle, P is the centre.
AB is a diameter.
PQ is a radius
MN is a chord
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त जिसका केंद्र 'P' है। इसमें 'AB' वृत्त का व्यास है, 'PQ' वृत्त की त्रिज्या है, और 'MN' वृत्त की एक जीवा (chord) है।
In simple words: A circle has a center, a radius from the center to any point on the edge, a diameter passing through the center connecting two points on the edge, and a chord connecting any two points on the edge.

🎯 Exam Tip: Clearly label the center, diameter, radius, and chord to demonstrate understanding of these fundamental geometric terms.

Relationship Between Radius And Diameter

Study the circle given alongside. Think over the following questions.

ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त जिसका केंद्र 'O' है और 'AB' उसका व्यास है जो वृत्त के केंद्र से होकर गुजरता है।

• Which are the radii in the circle?
• How many radii make up diameter AB?
• If the length of one radius is 3 cm, what is the length of the diameter?
• How long is the diameter as compared to the radius?

The diameter of a circle is twice the length of its radius.

• If another diameter CD is drawn on the same circle, will its length be the same as that of AB?

All the diameters of a circle are of the same length.

Test 1:

Measure the diameters and radii of the circles given below with a ruler and verify the relationship between their lengths.

Test 2:

1. Draw a circle on a piece of paper and cut it out.

ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त जिसका केंद्र 'P' है और 'AB' उसका व्यास है।

2. Name the centre of the circle P.

ℹ️ चित्र व्याख्या (Diagram Explanation): एक अर्धवृत्त जिसका केंद्र 'P' है, और 'AB' इसकी सीधी भुजा या व्यास है।

3. Draw the diameter of the circle and name it AB. Note that PA and PB are radii of the circle.

ℹ️ चित्र व्याख्या (Diagram Explanation): एक अर्धवृत्त जिसका केंद्र 'P' है, और 'AB' इसकी सीधी भुजा या व्यास है।

4. Fold the circular paper along AB as shown in the picture.

ℹ️ चित्र व्याख्या (Diagram Explanation): एक गोलाकार कागज जिसे व्यास के अनुदिश मोड़कर उसकी त्रिज्या को दर्शाया गया है।

Fold the paper at P in such a way that point B will fall on point A. Radius PB falls exactly on radius PA. In other words, they coincide.

From this, we can see that every radius of a circle is half the length of its diameter.

Circles Problem Set 28 Additional Important Questions And Answers

Question 1. Draw circles with the radii given below:
(1) 1.5 cm
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त जिसका केंद्र 'O' है और 'OD' उसकी त्रिज्या है जिसकी लम्बाई 1.5 सेमी है।
In simple words: This question requires drawing a circle with a radius of 1.5 cm. Use a compass to measure 1.5 cm and draw the circle.

🎯 Exam Tip: Precision in setting the compass to the given radius is key to drawing accurate circles.

(2) 2.3 cm
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त जिसका केंद्र 'O' है और 'OE' उसकी त्रिज्या है जिसकी लम्बाई 2.3 सेमी है।
In simple words: For a 2.3 cm radius, accurately open your compass to that measurement and draw the circle.

🎯 Exam Tip: Always double-check your compass measurement with a ruler before drawing to ensure accuracy.

Question 2. Which one of the following statement is true:
(1) All chords are diameters.
(2) All diameters are chords.
Answer: (2) All diameters are chords.
In simple words: A chord connects any two points on a circle, and a diameter is a special type of chord that passes through the center. Therefore, all diameters are chords, but not all chords are diameters.

🎯 Exam Tip: Understand the definitions of 'chord' and 'diameter'; a diameter is a chord that always passes through the center of the circle, making it the longest possible chord.

Class 5