Areas Related to Circles Class 10 Worksheet Maths

Multiple Choice Questions

Q2: If ‘r’ is the radius of a circle, then it's circumference is given by
(a) 2πr
(b) None of these
(c) πr
(d) 2πd
Ans: (a)

Sol: If the radius of a circle is given, the circumference or perimeter can be calculated using the formula below:-
Circumference = 2πr

Q3: The angle described by the minute hand between 4.00 pm and 4.25 pm is
(a) 900
(b) 1500
(c) 1250
(d) 1000
Ans: (b)
Sol: 
Time duration between 4.00 pm and 4.25 pm = 25 minutes
Angle described by minute hand in 60 minutes = 3600
Angle described by minute hand in 25 minutes = 3600/600 × 25 = 1500

Q4: If a line meets the circle in two distinct points, it is called(a) a chord
(b) a radius
(c) secant
(d) a tangent
Ans: (c)
Sol: A secant line, also simply called a secant, is a line meet two points in a circle. 

Q5: The perimeter of a protractor is
(a) πr
(b) πr+2r
(c) π+r
(d) π+2r
Ans: (b)
Sol: Let radius of the protractor be r ∴Perimeter of protractor = Perimeter of semicircle + Diameter of semicircle
⇒ Perimeter of protractor = πr + 2r

Q6: The perimeter of a circle having radius 5cm is equal to:
(a) 30 cm
(b) 3.14 cm
(c) 31.4 cm
(d) 40 cm
Ans: (c)
Sol: The perimeter of the circle is equal to the circumference of the circle.
Circumference = 2πr
= 2 x 3.14 x 5
= 31.4 cm

Q7: Area of the circle with radius 5cm is equal to:
(a) 60 sq.cm
(b) 75.5 sq.cm
(c) 78.5 sq.cm
(d) 10.5 sq.cm
Ans: (c)
Sol: Radius = 5cm
Area = πr² = 3.14 x 5 x 5 = 78.5 sq.cm

Q8: The largest triangle inscribed in a semi-circle of radius r, then the area of that triangle is;
(a) r²
(b) 1/2r²
(c) 2r²
(d) √2r²
Ans: (a) r²
Sol: The height of the largest triangle inscribed will be equal to the radius of the semi-circle and base will be equal to the diameter of the semi-circle.
Area of triangle = ½ x base x height
= ½ x 2r x r
= r²

Q9: If the perimeter of the circle and square are equal, then the ratio of their areas will be equal to:
(a) 14:11
(b) 22:7
(c) 7:22
(d) 11:14
Ans: (a) 
Sol: Given,
The perimeter of circle = perimeter of the square
2πr = 4a
a=πr/2
Area of square = a² = (πr/2)²
A_circle/A_square = πr²/(πr/2)²

= 14/11

Q10: The area of the circle that can be inscribed in a square of side 8 cm is
(a) 36 π cm²
(b) 16 π cm²
(c) 12 π cm²
(d) 9 π cm²
Ans: (b) 16 π cm²
Sol: Given,
Side of square = 8 cm
Diameter of a circle = side of square = 8 cm
Therefore, Radius of circle = 4 cm
Area of circle
= π(4)²
= π (4)²
= 16π cm²

Very Short Answer Question

Q1: A bicycle wheel makes 5000 revolutions in moving 11km.Find the diameter of the wheel.
Ans: 70 cm

Q2: A chord AB of a circle of radius 10 cm makes a right angle at the centre of the circle. Find the area of the minor and major segments.
Ans: 28.5cm², 285.5cm²

Q3: Find the difference of the areas of a sector of angle 1200 and its corresponding major sector of a circle of radius 21 cm.
Ans: 462cm²

Q4: A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.
Ans: 15.84 km/hr

Long Question Answer

Length of each side of the square sheet = 4r cm.

∴ Area of the square cardboard sheet = (4r 4r) cm² = 16 r² cm² 

But, the area of the cardboard sheet is given to be 784 cm² 

16r² = 784 r² = 49

r = 7

Area of one circular plate = = 154 cm

Area of four circular plates = 4× 154 cm² = 616 cm² 

Uncovered area of the square sheet = (784 - 616) cm² = 168 cm².