Maharashtra Board Class 5 Maths Chapter 7 Circles Set 31 Solutions

Std 5 Maths Chapter 7 Circles

Question 1. In the figure given alongside, points S, L, M, and N are on the circle. Answer the questions with the help of the diagram.
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त दिखाया गया है जिस पर S, L, M और N बिंदु स्थित हैं। ये बिंदु वृत्त की परिधि पर क्रमानुसार दिखाए गए हैं और वृत्त को विभिन्न चापों में विभाजित करते हैं।
(1) Write the names of the arcs with end-points S and M.
Answer: Arcs with the end-points S and M are, arc SLM and arc SNM.
(2) Write the names of the arcs with end-points L and N.
Answer: Arcs with the end-points L and N are, arc LMN and arc LSN.
In simple words: The questions ask to identify arcs based on given end-points on a circle. An arc is a portion of the circumference, and there are typically two arcs between any two points on a circle (a major and a minor arc), unless the points form a diameter.

🎯 Exam Tip: When naming arcs, always mention the three points (start, a point in between, and end) to avoid ambiguity between major and minor arcs, especially for longer arcs. For simple cases like these, SLM and SNM clearly delineate the two possibilities.

 

Question 2. Write the names of arcs that points A, B, C, and D in the given circle give rise to.
Answer: Arcs with end-points A and C are, arc ABC and arc ADC.
Arcs with end-points B and D are, arc BAD and arc BCD.
In simple words: Just like with S and M, for any two points on a circle, there are two distinct arcs connecting them. The question requires listing these pairs of arcs using the given points A, B, C, and D.

🎯 Exam Tip: Remember that two points on a circle define two arcs. To differentiate them, you must use an intermediate point from the arc in its name (e.g., arc ABC vs. arc ADC).

 

Question 3. Give the names of the arcs that are made by points P, Q, R, S, and T in the figure.
Answer: Taking end-points : P and R, arc PQR, arc PTR.
Taking end-points: Q and S, arc QRS, arc QTS
Taking end-points : R and T, arc RST, arc RPT
Taking end-points : S and P, arc STP, arc SRP
Taking end-points: Q and T, arc QPT, arc QST
In simple words: This question extends the previous concept to five points on a circle. For each possible pair of end-points, two arcs are formed, and the answer lists these pairs by specifying a point in between the end-points for each arc.

🎯 Exam Tip: Systematically choose pairs of points as end-points and then identify the two arcs for each pair. Ensure all unique pairs of end-points are covered to get full marks.

 

Question 4. Measure and note down the circumference of different circular objects. (It is convenient to use a measuring tape for this purpose.)
Answer: This question requires practical activity, not a theoretical answer. It's an experimental exercise for students.
In simple words: This question is a hands-on activity where you measure the distance around circular objects using a measuring tape. It helps you understand what circumference means in real life.

🎯 Exam Tip: This type of question tests practical application. Focus on accurate measurement and clear recording of your findings. While not typically a written exam question, understanding the concept is crucial.

Chapter 7 Circles Problem Set 31 Additional Important Questions and Answers

 

Question 1. Draw circles with the radii given below:
(1) 1.2 cm
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त दिखाया गया है जिसका केंद्र O है और त्रिज्या 1.2 सेमी है। बिंदु A वृत्त की परिधि पर स्थित है, जो केंद्र O से 1.2 सेमी की दूरी पर है।
(2) 2.5 cm
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त दर्शाया गया है जिसका केंद्र O है और त्रिज्या 2.5 सेमी है। बिंदु P वृत्त की परिधि पर स्थित है, जो केंद्र O से 2.5 सेमी की दूरी पर है।
(3) 3.3 cm
Answer:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त प्रदर्शित है जिसका केंद्र O है और त्रिज्या 3.3 सेमी है। बिंदु M वृत्त की परिधि पर स्थित है, जो केंद्र O से 3.3 सेमी की दूरी पर है।
In simple words: To draw a circle with a given radius, you use a compass. Set the compass opening to the specified radius (e.g., 1.2 cm), place the sharp point at the center, and draw a full rotation.

🎯 Exam Tip: Use a sharp pencil and a compass for accuracy. Clearly mark the center and the radius value on your diagram. Ensure your circles are complete and neatly drawn.

 

Question 2. Write true or false for the following statements:
(1) Longest chord is a diameter.
(2) Centre is not lying on the diameter.
(3) All chords are of equal length.
(4) All chords passes through the centre.
Answer:
(1) True
(2) False
(3) False
(4) False
In simple words: A diameter is a special type of chord that passes through the center, and it's always the longest chord in any circle. The center always lies on the diameter, and chords can be of different lengths and do not necessarily pass through the center.

🎯 Exam Tip: Understand the definitions of radius, chord, and diameter. These fundamental concepts are frequently tested for basic understanding of circles.

 

Question 3. Match the cplumns (A) and (B):

(A)	(B)
(1) OP	(a) centre
(2) O	(b) diameter
(3) XY	(c) radius
(4) QR	(d) chord

ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त दर्शाया गया है जिसका केंद्र O है। वृत्त की परिधि पर P और R बिंदु स्थित हैं। रेखाखंड QR केंद्र O से होकर गुजरता है, जिससे यह वृत्त का व्यास बनता है। रेखाखंड OP वृत्त की त्रिज्या है। X और Y बिंदु वृत्त के बाहर स्थित हैं, जहाँ XY एक जीवा के रूप में दर्शाया गया है।
Answer:
(1) ↔ (c),
(2) ↔ (a),
(3) ↔ (d),
(4) ↔ (b)
In simple words: This question tests your ability to identify parts of a circle from a diagram. OP is a line from the center to the circumference (radius), O is the center point, XY connects two points on the circumference (chord), and QR passes through the center connecting two points on the circumference (diameter).

🎯 Exam Tip: Clearly differentiate between radius, chord, and diameter. A diameter is a special chord, and a radius connects the center to the circumference. Practice identifying these elements in various diagrams.

 

Question 4. Complete the following table by filling in the blanks:

Radius	3 cm		17 cm
Diameter		20 cm		18 cm

Answer:
(1) 6 cm
(2) 10 cm
(3) 34 cm
(4) 9 cm
In simple words: The diameter of a circle is always twice its radius, and conversely, the radius is half of the diameter. Use this relationship (Diameter = 2 × Radius or Radius = Diameter / 2) to fill in the missing values.

🎯 Exam Tip: Remember the core relationship: Diameter = 2 × Radius. This formula is fundamental for solving problems involving circle measurements. Be careful with unit consistency.

 

Question 5. From the following figure, fill in the blanks:
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त प्रदर्शित है जिसका केंद्र O है। बिंदु P वृत्त के बाहर स्थित है। A और B बिंदु वृत्त की परिधि पर स्थित हैं, जहाँ रेखाखंड AB वृत्त के केंद्र O से होकर गुजरता है, जिससे यह वृत्त का व्यास बनता है।
(1) If OP = 4cm then AB = _______ cm, OA = _______ cm, OB = _______ cm.
(2) If AB = 10 cm then OA = _______ cm, OB = _______ cm, OP = _______ cm.
Answer:
(1) AB = 8 cm, OA = 4 cm, OB = 4 cm
(2) OA = 5 cm, OB = 5 cm, OP = 5 cm
In simple words: In a circle, all radii are equal. The diameter is twice the radius. If OP is a radius, then AB (diameter) is 2*OP. If AB is a diameter, then OA, OB, and OP (if O is center and P is on circumference) are all radii, meaning half of AB.

🎯 Exam Tip: Understand that OA, OB, and OP (when P is on the circumference) are all radii. The diameter AB is always twice the radius. This understanding helps in quickly filling the blanks.

 

Question 6. In the table below, write the names of the points in the interior and exterior of the circle and those on the circle.

Diagram	Points in the interior of the circle	Points in the exterior of the circle	Points on the circle
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त दिखाया गया है जिसका केंद्र O है। बिंदु A, F और G वृत्त के बाहरी क्षेत्र में स्थित हैं। बिंदु C, D और H वृत्त की परिधि पर स्थित हैं, जबकि बिंदु O, E और B वृत्त के आंतरिक क्षेत्र में स्थित हैं।

Answer: Points in the exterior of the circle are A, F and G.
Points in the interior of the circle are O, E and B, and Points on the circle are C, D and H.
In simple words: Points inside the circle are in its interior, points outside are in its exterior, and points lying exactly on the boundary of the circle are considered to be 'on' the circle.

🎯 Exam Tip: Visually identify the location of each point relative to the circle's boundary. Be precise in categorizing them into interior, exterior, or on the circle, as common errors can occur with points very close to the edge.

 

Question 7. Radius of a circle with centre P is 4 cm. Fill in the blanks.
(1) The, point A is at a distance of 5 cm from the centre P. Flence the point A lies in the _______ of the circle.
(2) Point B is at a distance of 4 cm. from the centre P. Hence the point B lies _______ circle.
(3) Point C lies at a distance 3 cm from the centre P. Hence it lies in the _______ of the circle.
Answer:
(1) Exterior
(2) on the circle
(3) interior
In simple words: If a point's distance from the center is greater than the radius, it's outside (exterior). If the distance equals the radius, it's on the circle. If the distance is less than the radius, it's inside (interior).

🎯 Exam Tip: Compare the given distance of a point from the center with the radius. If distance > radius, it's exterior. If distance = radius, it's on the circle. If distance < radius, it's interior.

 

Question 8. Solve the following:
(1) What is the length of the diameter of a circle of radius 6 cm?
(2) What is the length of the radius of a circle of diameter 14 cm?
(3) Give the names of the arcs that are made by points X, Y, Z and W in this picture.
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त प्रदर्शित है जिस पर X, Y, Z और W बिंदु स्थित हैं। ये बिंदु वृत्त की परिधि पर क्रमानुसार दिखाए गए हैं और वृत्त को विभिन्न चापों में विभाजित करते हैं।
(4) Give the names of the arc that are made by points E, F, G and H, taking end points E and G.
ℹ️ चित्र व्याख्या (Diagram Explanation): एक वृत्त दिखाया गया है जिस पर E, F, G और H बिंदु स्थित हैं। ये बिंदु वृत्त की परिधि पर क्रमानुसार दिखाए गए हैं और वृत्त को विभिन्न चापों में विभाजित करते हैं, जिसमें E और G अंतिम बिंदु हैं।
(5) If the diameter of a circle is 7 cm. what is the length of the circumference? (Use measure tap)
Answer:
(1) 12 cm
(2) 7 cm
(3) Having end-points X and Z, arc XYZ and arc XWZ
Having end-points Y and W, arc YZW and arc YXW
(4) By end-points E and G, arc EFG and arc EHG
(5) 22 cm
In simple words: This question combines basic circle concepts: diameter is twice the radius, radius is half the diameter, naming arcs, and understanding circumference. Circumference can be approximated practically using a measuring tape.

🎯 Exam Tip: Ensure you accurately calculate diameter/radius using the 2R=D relationship. When naming arcs, use three points to specify the path. For circumference, remember it's the distance around the circle, and for simple cases, practical measurement is expected.