Maharashtra Board Class 7 Chapter 11 Set 43 Circle Solutions

Question 1. Choose the correct option. If arc AXB and arc AYB are corresponding arcs and m(arc AXB) = 120° then m(arc AYB) =
(A) 140°
(B) 60°
(C) 240°
(D) 160°
Answer: (C) 240°
In simple words: The sum of the measures of a major arc and its corresponding minor arc is 360°. So, if the minor arc (AXB) is 120°, the major arc (AYB) is calculated as 360° - 120° = 240°.

🎯 Exam Tip: Remember that corresponding arcs always add up to 360 degrees, which is the full measure of a circle. This concept is fundamental for solving arc-related problems.

Question 2. Some arcs are shown in the circle with centre 'O' Write the names of the minor arcs, major arcs and semicircular arcs from among them.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक वृत्त है जिसका केंद्र 'O' है। वृत्त पर विभिन्न बिंदु P, X, Q, R, Y अंकित हैं। ये बिंदु वृत्त को कई छोटे और बड़े चापों में विभाजित करते हैं, जैसे QXP, PR, RY, YQ, QX, XP, PRY, PYQ, PQR, RQY, XPQ, XQP, XQR, QPR, QYR।
Answer: Minor arcs: arc QXP, arc PR, arc RY, arc YQ, arc QX, arc XP, arc PRY.
Major arcs : arc PYQ, arc PQR, arc RQY, arc XPQ, arc XQP, arc XQR
Semicircular arcs : arc QPR, arc QYR.
In simple words: Minor arcs are less than 180°, major arcs are greater than 180°, and semicircular arcs are exactly 180° (formed by a diameter). The listed arcs are categorized based on their span around the center 'O'.

🎯 Exam Tip: Carefully observe the positions of the points on the circle to correctly identify and name minor, major, and semicircular arcs. A diameter always divides a circle into two semicircular arcs.

Question 3. In a circle with centre O, the measure of a minor arc is 110°. What is the measure of the major arc PYQ?
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक वृत्त है जिसका केंद्र 'O' है। वृत्त पर बिंदु X, P, Q, Y, R अंकित हैं। इसमें एक लघु चाप (minor arc) दर्शाया गया है जिसका माप 110° है, और एक दीर्घ चाप (major arc) PYQ भी है जिसका माप ज्ञात करना है।
Answer: Measure of major arc = 360° - measure of corresponding minor arc
m (arc PYQ) = 360 - 110
m (arc PYQ) = 250°
The measure of the major arc PYQ is 250°.
In simple words: A major arc and its corresponding minor arc together form a full circle, which measures 360°. If the minor arc is 110°, the major arc will be 360° minus 110°, which is 250°.

🎯 Exam Tip: Always remember the relationship between a minor arc and its corresponding major arc; their sum is always 360°. This formula is key for calculating unknown arc measures.

Maharashtra Board Class 7 Maths Chapter 11 Circle Practice Set 43 Intext Questions And Activities

Question 1. Measure the circumference and diameter of the objects given below and enter the ratio of the circumference to its diameter in the table.

Examine the ratio of the circumference to the diameter. What do we see? (Textbook pg. no. 75)
Answer: The ratio of circumference to the diameter is same and is approximately equal to 3.14.
In simple words: This activity demonstrates that for any circular object, the ratio of its circumference to its diameter is a constant value, approximately 3.14, known as Pi (π).

🎯 Exam Tip: Understanding that the ratio of circumference to diameter is a constant (Pi) is crucial. This foundational concept forms the basis for calculating circumference and area of circles.

Question 2. Place a cylindrical bottle on a paper and trace the outline of its base. Use a thread to measure the circumference of the circle. (Textbook pg. no. 75)
Answer: (Students should attempt the above activities on their own)
In simple words: This activity involves practically tracing a circular object and using a thread to measure its boundary (circumference), helping to understand the concept of circumference directly.

🎯 Exam Tip: Hands-on activities like this reinforce theoretical knowledge by allowing students to directly experience and measure geometric properties. Practice precision in measurement.

Question 3. Measure the circumference of a bangle with the help of a thread. (Textbook pg. no. 75)
Answer: (Students should attempt the above activities on their own)
In simple words: This activity teaches how to measure the circumference of a circular object like a bangle using a simple thread, providing practical experience with real-world geometric measurements.

🎯 Exam Tip: Practical measurement skills are important. When measuring with a thread, ensure it's taut and carefully marked for accuracy, as small errors can lead to significant deviations.

Question 4. Measure the circumference of any cylindrical object using a thread. (Textbook pg. no. 75)
Answer: (Students should attempt the above activities on their own)
In simple words: This general activity encourages students to apply the thread measurement technique to any cylindrical object, reinforcing the practical skill of measuring circumference.

🎯 Exam Tip: The ability to measure circumference using simple tools like a thread is a valuable skill. Focus on consistent technique and accurate reading to get reliable results.