Unit Test: Areas Related to Circles | Mathematics (Maths) Class 10 PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers 9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Q1: If the perimeter of the circle and square are equal, then the ratio of their areas will be equal to: (1 Mark)

(a) 14:11
(b) 22:7
(c) 7:22
(d) 11:14

Q2: The area of the circle that can be inscribed in a square of side 8 cm is (1 Mark)

(a) 36 π cm²
(b) 16 π cm²
(c) 12 π cm²
(d) 9 π cm²

Q3: The area of a sector of a circle with radius 6 cm if the angle of the sector is 60°.  (1 Mark)

(a) 142/7
(b) 152/7
(c) 132/7
(d) 122/7

Q4: In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The area of the sector formed by the arc is:  (1 Mark)

(a) 200 cm²
(b) 220 cm²
(c) 231 cm²
(d) 250 cm²

Q5: If the area of a circle is 154 cm2, then its perimeter is  (1 Mark)

(a) 11 cm
(b) 22 cm
(c) 44 cm
(d) 55 cm

Q6: What is the area of a circle whose circumference is 44 cm?  (2 Marks)

Q7: Find the area of the sector of a circle with a radius of 4 cm and of angle 30°. Also, find the area of the corresponding major sector (Use π = 3.14) (2 Marks)

Q8: Calculate the area of a sector of angle 60°. Given, the circle has a radius of 6 cm. (2 Marks)

Q9: Calculate the perimeter of an equilateral triangle if it inscribes a circle whose area is 154 cm²  (3 Marks)  

Q10: Find the Radius of a circle whose Circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm. (3 Marks)

​Q11: A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.  (Use π = 3.14 and √3 = 1.73) (3 Marks)

Q12: A chord of a circle of Radius 10 cm subtends a right angle at the center. Find the Area of the corresponding: (5 Marks)

(i) minor segment
(ii) major sector. (Use π = 3.14)

Q13: A chord of the circle of Radius 15 cm makes the angle of 60° at the center. Find out the areas for the corresponding minor and the major segments of the circle. (Use π = 3.14 and √3 = 1.73) (5 Marks)

You can find the solutions of this Unit Test here: Unit Test (Solutions): Areas Related to Circles