CBSE Class 10 Mathematics Area Related To Circle Worksheet Set 01

ASSERTION AND REASONING

Question. Assertion : If a wire of length 22 cm is bent in the shape of a circle, then area of the circle so formed is 40 𝑐m².
Reason : Circumference of the circle = length of the wire.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true
Answer : D

Question. Assertion : In a circle of radius 6 cm, the angle of a sector is 60° Then the area of the sector is 18 67 cm².
Reason : Area of the circle with radius 𝑟 is 𝜋𝑟² .
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : B

Question. Assertion : If the circumference of a circle is 176 cm, then its radius is 28 cm.
Reason : Circumference= 2 × 𝜋 × 𝑟𝑎𝑑𝑖𝑢𝑠
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : A

Question. Assertion : If the outer and inner diameter of a circular path is 10 m and 6 m then area of the path is 16𝜋 m² .
Reason : If R and r be the radius of outer and inner circular path, then area of path is 𝜋(𝑅²− 𝑟²)
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) ) Assertion (A) is false but reason (R) is true
Answer : A

Question. Assertion : The area of circular playground is 22176 m² the cost of fencing this ground at the rate Rs. 50 per metre is Rs. 26400
Reason : If R and r be the radius of outer and inner circular path ,then the area of the ring will be π(R²– r²)
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : B

CASE STUDY QUESTION 

Q1. Raksha Bandhan, is a popular annual rite, or ceremony, which is celebrated in South Asia, and in other parts of the world significantly influenced by Hindu culture. On this day, sisters of all ages tie a talisman, or amulet, called the rakhi, around the wrists of their brothers, symbolically protecting them, receiving a gift in return, and traditionally investing the brothers with a share of the responsibility of their potential care..

Observe the 2 designs of Rakhi
Design A: Rakhi A is made with silver wire in the form of a circle with diameter 28mm. The wire used for making 4 diameters which divide the circle into 8 equal parts.
Design B: Rakhi B is made of two colours - Gold and silver. Outer part is made with Gold. The circumference of silver part is 44mm and the gold part is 3mm wide everywhere.

Refer to Design A

(a). Find the total length of silver wire required
Answer : 200 mm

(b) Find the area of each sector of the Rakhi
Answer : 77 mm²

Refer to Design B

(c) Find the circumference of outer part (golden)
Answer : 62.86 mm

Please click on below link to download CBSE Class 10 Mathematics Area Related To Circle Worksheet Set A