Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Worksheet Solutions: Areas Related to Circles

Areas Related to Circles Class 10 Worksheet Maths

Multiple Choice Questions

Q1: The part of the circular region enclosed by a chord and the corresponding arc of a circle is called
(a) a segment
(b) a diameter
(c) a radius
(d) a sector

Ans: (a)The part of the circular region enclosed by a chord and the corresponding arc of a circle is called a segment.

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) √2r
2
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
Acircle/Asquare = 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


Q1: On a square cardboard sheet of area 784 cm2, four circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to circular plates. Find the area of the square sheet not covered by the circular plates.
Ans: 
Let the radius of each circular plate be r cm. Then,

Areas Related to Circles Class 10 Worksheet MathsLength 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 cm

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.

The document Areas Related to Circles Class 10 Worksheet Maths is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Areas Related to Circles Class 10 Worksheet Maths

1. What is the formula to find the area of a circle?
Ans. The formula to find the area of a circle is A = πr^2, where A represents the area and r represents the radius of the circle.
2. How do you find the circumference of a circle?
Ans. The circumference of a circle can be found using the formula C = 2πr, where C represents the circumference and r represents the radius of the circle.
3. Can you find the area of a circle if only the diameter is given?
Ans. Yes, the area of a circle can be found if the diameter is given. The formula to find the area using the diameter is A = π(d/2)^2, where A represents the area and d represents the diameter of the circle.
4. How do you find the area of a sector of a circle?
Ans. The area of a sector of a circle can be found using the formula A = (θ/360)πr^2, where A represents the area, θ represents the central angle in degrees, and r represents the radius of the circle.
5. Can you find the area of a circle if only the circumference is given?
Ans. No, the area of a circle cannot be directly found if only the circumference is given. However, the radius can be determined using the formula C = 2πr, and then the area can be calculated using the formula A = πr^2.
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