Area problems
- 1. A circular road runs rounds a circular ground. If the difference between the circumference of the outer circle and the inner circle is 66 meters, the width of the road is?
Options- A. 21 meters
- B. 10.5 meters
- C. 7 meters
- D. 5.25 meters Discuss
Correct Answer: 10.5 meters
Explanation:
Let outer radius be R and inner radius be r.
Then from question
2?R - 2?r = 66
? 2? (R-r) = 66
? (2 x 22)/7 x (R - r) = 66
? (R-r) = (66 x 7) / 44
= 10.5 m
- 2. The inner circumference of a circular race track, 14 m wide is 440 m . Then the radius of the outer circle is?
Options- A. 70 m
- B. 56 m
- C. 77 m
- D. 84 m Discuss
Correct Answer: 84 m
Explanation:
Circumference of a circular = 2?r
? 2 x (22 / 7) x r = 440
? r = [440 x (7/22) x (1/2)] = 70 m
? Radius of outer circle = (70 + 14) m
= 84 m
- 3. The ratio of the radii of two circle is 1:3 the radio of their areas is?
Options- A. 1:3
- B. 1:6
- C. 1:9
- D. None of these Discuss
Correct Answer: 1:9
Explanation:
The Radio of areas = area of first circle : area of 2nd circle
= ?r2 / ?(3r)2
= ?r2/ 9 ?r2
= 1/9
= 1: 9
- 4. The Area of a square is 50 sq. units. Then the area of the circle drawn on its diagonal is?
Options- A. 25? sq. units
- B. 100? sq. units
- C. 50? sq. units
- D. None of theas Discuss
Correct Answer: 25? sq. units
Explanation:
Area = (Diagonal)2 / 2 = 50
? Diagonal = 10 units
? Radius of required circle = 5 units
Its area = [? x (5)2 ] cm2
= 25? units2
- 5. A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6: 5 . The smaller side of the rectangle is?
Options- A. 30 cm
- B. 60 cm
- C. 72 cm
- D. 132 cm Discuss
Correct Answer: 60 cm
Explanation:
Perimeter of rectangle = Circumference of circle
= 2?r
=2 x ( 22/7 ) x 42
= 264 cm
Now perimeter of rectangle = 2 x ( 6a + 5a )
? 2 x (6a + 5a) = 264
? a = 12
Smaller side of rectangle = 5a
= 60 cm
- 6. If 88 m wire is required to fence a circular plot of land, then the area of the plot is?
Options- A. 526 m2
- B. 556 m2
- C. 616 m2
- D. None of these Discuss
Correct Answer: 616 m2
Explanation:
Circumference of circular plot= 88 m
? 2 x (22/7) x r = 88
? r = 88 x (7/22) x (1/2) = 14 m
Now area = ?r2
=( 22/7) x 14 x 14 m2
= 616 m2
- 7. If the circumference of a circle is increased by 50%, then its area will be increased by?
Options- A. 50%
- B. 100%
- C. 125%
- D. 225% Discuss
Correct Answer: 125%
Explanation:
Original circumference = 2?r
New circumference = (150 /100) x 2 ?r
= 3?r
2?R = 3?r
? R = 3r/2
Original area = ?r2
New area = ?R2
= ?9r2 / 4 = 9?r2/4
Increase in area = (9?r2/4 ) - (?r2)
= (5/4) ?r2
Req. increase per cent = [{(5/4) ?r2} / {?r2}] x 100
= 125 %
- 8. If a regular hexagon is inscribed in a circle of radius, r then its perimeter?
Options- A. 3r
- B. 6r
- C. 9r
- D. 12r Discuss
Correct Answer: 9r
Explanation:
Length of each side of hexagoan = radius of circle
? its perimeter = 6r
- 9. Four horses are be tethered at four concern of a square plot of side 63 meters, so that they just cannot reach one another. The area left ungrazed is?
Options- A. 675.5 m2
- B. 780.6 m2
- C. 785.8 m2
- D. 850.5 m2 Discuss
Correct Answer: 850.5 m2
Explanation:
Area left ungrazed
= [(63 x 63) - (4 x 1/4 x 22/7 x (63/2)2] m2
= (63 x 63 - (99 x 63)/2 ) m2
= 63 x (63 - 99/2) m2
= 850.5 m2
- 10. The circumferences of two concentric are 176 m and 132 m respectively. what is the difference between their radii?
Options- A. 5 meter
- B. 7 meter
- C. 8 meter
- D. 44 meter Discuss
Correct Answer: 7 meter
Explanation:
? 2?R - 2?r = (176-132)
? 2?(R-r) = 44
? R-r = ( 44 x 7 )/ (2 x 22)
= 7 m
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