Circles (Area and Perimeter)
Question
Q1.
Find the area of a quadrant of a circle whose circumference is 44 cm.
(a) 98 cm2 (b) 38.5 cm2
(c) 40 cm2 (d) 42.5 cm2
Solution.
2 π r = 44
2 x 22/7 x r = 44
r = 7
Area of quadrant = 1/4 π r2
= 1/4 x 22/7 x 49
= 154/4
= 77/2
= 38.5 cm2
Solution
Q2.
Find the area of a quadrant of a circle whose circumference is 44 cm.
(a) 98 cm2 (b) 38.5 cm2
(c) 40 cm2 (d) 42.5 cm2
Solution.
2 π r = 44
2 x 22/7 x r = 44
r = 7
Area of quadrant = 1/4 π r2
= 1/4 x 22/7 x 49
= 154/4
= 77/2
= 38.5 cm2
Solution
Q3.
Formula of perimeter of a semi-circle having radius r.
(a) πr (b) 2r (c) 2πr (d) πr + 2r
Answer.
(d) πr + 2r
Solution
Q4.
The area of a circle of radius 10 is numerically what percent of its circumference ?
(a) 400 (b) 300 (c) 500 (d) 200
Answer.
(c) 500
Solution
Q5.
If the area of a sector of a circle is 7/12 of the area of circle, then the angle subtended to sector on center is
(a) 90o (b) 210o (c) 180o (d) 20o
Solution.
(θ/360 π r2)/π r2 = 7/12
θ/360o = 7/12
θ/30o = 7
θ = 210o
Solution
Q6.
A wheel has diameter 84 cm. find how many complete revolutions must it take to cover 396 meters.
(a) 250 (b) 100
(c) 50 (d) 150
Solution.
circumference of the wheel = 2πr = 2.64 m
total numbers of wheel = 396/2.64 = 150
Solution
Q7.
Find the area of two quadrants whose circumference is 88 cm.
(a) 390 cm2 (b) 300 cm2
(c) 308 cm2 (d) 380 cm2
Solution.
2πr = 88
(2 x 22 x r)/r = 88
r = 14 cm
Area of two quadrants = 1/2 π r2
1/2 x 22/7 x 14 x 14
= 22 x 14
= 308 cm2
Solution
Q8.
The perimeter of a sector of a circle of radius π is (5 π)/2 . find the area of the sector .
(a)
2 π2 (b) (1/2) π2 (c) π2 (d) (1/4) π2
Solution.
2r + arc length = (5π)/2
2π + arc length = (5π)/2
arc length = (5π)/2 - 2π
Area of the sector = (1/2) rl = (1/2)π x (π/2)
= (1/4) π2
Solution
Q9.
The radius of a circle is increased by 8%, find the percentage change in its area.
(a) 19.6% (b) 22% (c) 16.64%
(d) 10%
Solution.
(c) 16.64%
Solution
Q10.
Two circles touches externally. Sum of their areas is 130πm2. The distance between their centers is 14 m . Find the radius of smaller
circle.
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
(c) 3
Solution
