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 = πr^{2} = 3.14 x 5 x 5 = 78.5 sq.cm
Q8: The largest triangle inscribed in a semicircle of radius r, then the area of that triangle is;
(a) r^{2}
(b) 1/2r^{2}
(c) 2r^{2}
(d) √2r^{2}
Ans: (a) r^{2}
Sol: The height of the largest triangle inscribed will be equal to the radius of the semicircle and base will be equal to the diameter of the semicircle.
Area of triangle = ½ x base x height
= ½ x 2r x r
= r^{2}
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 = a^{2} = (πr/2)^{2}
A_{circle}/A_{square} = πr^{2}/(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 cm^{2}
(b) 16 π cm^{2}
(c) 12 π cm^{2}
(d) 9 π cm^{2}
Ans: (b) 16 π cm^{2}
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 cm^{2}
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: 28.5cm^{2}, 285.5cm^{2}
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: 462cm^{2}
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
Length of each side of the square sheet = 4r cm.
∴ Area of the square cardboard sheet = (4r 4r) cm^{2} = 16 r^{2} cm^{2}
But, the area of the cardboard sheet is given to be 784 cm^{2 }
16r^{2} = 784 r^{2} = 49
r = 7
Area of one circular plate = = 154 cm
Area of four circular plates = 4× 154 cm^{2} = 616 cm^{2}
Uncovered area of the square sheet = (784  616) cm^{2} = 168 cm^{2}.
116 videos420 docs77 tests

1. What is the formula to find the area of a circle? 
2. How do you find the circumference of a circle? 
3. Can you find the area of a circle if only the diameter is given? 
4. How do you find the area of a sector of a circle? 
5. Can you find the area of a circle if only the circumference is given? 

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