Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Value Based Questions: Areas Related to Circles

Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

Q1. Shankar wants a lawn to be developed in a corner of his square plot. He gave following three options to the lawn-developer:

Class 10 Maths Chapter 11 Question Answers - Areas Related to CirclesClass 10 Maths Chapter 11 Question Answers - Areas Related to CirclesClass 10 Maths Chapter 11 Question Answers - Areas Related to Circles

The lawn developing rate is Rs 150 per sq. m and the lawn under option-III was developed, however, Shankar paid for the option having largest area. The lawn-developer realized the mistake and refunded the balance back to Shankar.
 (a) Find the area in each of the above three options.
 (b) What amount was refunded back to Shankar by the lawn-developer?
 (c) Which mathematical concept is used in above problem?
 (d) Refunding the difference, which value is depicted by the lawn-developer?

Sol. (a) Area of lawn in option-I = 1/4 (πr2)

Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles
Area of lawn in option-II = 7 × 7 m2 = 49 m2

Area of lawn in option-III =  Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles
(b) ∵ Largest area of the lawn = 49 m2
Cost of lawn-developing in option-II = Rs 150 × 49 = Rs 7350
∵ Area of lawn in option-III = 24.5 m2
∴ Cost of lawn-developing in option-III
Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

⇒ Amount refunded back by the lawn-developer = Rs 7350 – Rs 3675 = Rs 3675
(c) Areas related to plane surfaces.
(d) Honesty

Q2. Shivram has a piece of land in the form of sector OBPQ adjoining to a temple. He donates a part of it to the temple such that a square plot OABC is left with him.
 If OA = 20 m. Then,
 (a) Find the area of the shaded region (donated to the temple). [use π = 3.14]
 (b) Which mathematical concept is used in above problem?
 (c) By donating land to a temple by Shivram, which value is depicted?

Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

Sol. (a) ∵ OABC is a square and OA = 20 m
∴ Diagonal OB of the square OABC
Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

⇒ Radius of the quadrant OPBQ =  Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

⇒ Area of the quadrant OPBQ  Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles
Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

Also, area of square OABC = 20 × 20 m2 = 400 m2
∴ Area of the shaded region = [Area of the quadrant OPBQ] – [Area of the square OABC]
= 628 m2 – 400 m2 = 228 m2

Thus, area of the land donated to the temple = 228 m2
(b) Related to circles
(c) Charity.

Q3. Rajat has a piece of land in the shape of a rectangle with two semicircles on its smaller sides, as diameters, added to its outside. The sides of the rectangle are 36 m and 21 m. He lets out the two semicircular parts at the rate of Rs 100 per sq. metre and donates the proceeds to an orphanage.

Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

(a) Find the total area of his land. [use π = 22/7]
 (b) What amount does he donate to orphanage?
 (c) Which mathematical concept is used in the above problem?
 (d) By donating the rent proceeds to an orphanage which value is depicted by Rajat?

Sol. (a) Area of the rectangular part = 36 × 24.5 m2

Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

Area of both the semicircular parts =  Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles
Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

∴ Area of Rajat’s total land = 882 m2 + 1386 m2 = 2268 m2
(b) ∴ Rent rate = Rs 100 per m2
∴ Total rent = Rs 1386 × 100 = Rs 1,38,600
⇒ Amount donated to orphanage by Rajat = Rs 1,38,600
(c) Areas related to circles

Q4. Rajesh has a circular plot of radius 105m. He donates a 7m wide track along its boundary for community-track.

Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

(a) Find the area of the track. [use π = 22/7]
 (b) Which mathematical concept is used in the above problem?
 (c) By donating a community-track, which value is depicted by Rajesh?

Sol. (a) Radius of the total circular plot = 105 m
∴ Area of the total circular plot = π (105)2 sq. m
∴ Width of the track = 7 m
∴ Radius of the circular plot excluding the track
= 105 m – 7 m = 98 m
⇒ Area of the inner circular plot = π (98)2 sq. m.
Now, area of the track = [Area of total circular plot] – [Area of inner circular plot]
= π (105)2 – π (98)2 sq. m
= π [1052 – 982] sq. m
= π [(105 – 98) (105 + 98)] sq. m
[using a2 – b2 = (a–b) (a+b)]

= π [7 × 203] sq. m
Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

= 22 × 203 sq. m
= 4466 sq. m

(b) Areas related to circles
(c) Community service

The document Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Class 10 Maths Chapter 11 Question Answers - Areas Related to Circles

1. What is the formula to find the circumference of a circle?
Ans. The formula to find the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius of the circle.
2. How is the area of a circle calculated?
Ans. The area of a circle is calculated using the formula A = πr^2, where A represents the area and r represents the radius of the circle.
3. How do you find the diameter of a circle if you know the radius?
Ans. To find the diameter of a circle if you know the radius, you simply double the value of the radius. Therefore, the diameter (D) is equal to 2r, where r represents the radius.
4. Can the circumference of a circle be greater than its diameter?
Ans. No, the circumference of a circle cannot be greater than its diameter. The ratio of the circumference to the diameter of any circle is always constant and equal to π (pi), which is approximately 3.14.
5. What is the relationship between the radius and diameter of a circle?
Ans. The radius of a circle is half the length of its diameter. In other words, if you know the diameter (D) of a circle, you can find the radius (r) by dividing the diameter by 2, and vice versa.
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