Area problems
- 1. The area of a circle is increased by 22 sq cm when its radius is increased by 1 cm. Find the original radius of the circle.
Options- A. 6 cm
- B. 3.2 cm
- C. 3 cm
- D. 3.5 cm Discuss
Correct Answer: 3 cm
Explanation:
Let original radius be r.
Then, according to the questions,
? (r + 1)2 - ?r2 = 22
? ? x [(r + 1)2 - r2] = 22
? (22/7) x (r + 1 + r ) x (r + 1 - r) = 22
? 2r + 1 = 7
? 2r = 6
? r = 6/2 = 3 cm
- 2. Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 154 sq m.
Options- A. 7 m
- B. 8 m
- C. 12 m
- D. 13 m Discuss
Correct Answer: 7 m
Explanation:
Length of to the rope = Radius of circle
According to the question,
?r2 = 154
? r2 = 154 x (7/22) = 7 x 7 = 49
? r = ?49 = 7 m
- 3. A man riding a bicycle, completes one lap of a circular field along its circumference at the speed of 14.4 km/h in 1 min 28 s. What is the area of the field?
Options- A. 7958 sq m
- B. 9856 sq m
- C. 8842 sq m
- D. Cannot be determined Discuss
Correct Answer: 9856 sq m
Explanation:
The man takes 3600 s for 14.4 km
The man will take 88 s for
14.4 x (88/3600) = 352/1000 km = 352 m
Now, circumference of circular field = 352 m
? 2?r = 352 m
2 x (22/7) x r = 352
? r = 56 m
Therefore, area of the field = ?r2
= (22/7) x 56 x 56
= 8 x 22 x 56 m2
= 9856 sq m.
- 4. A person observed that he required 30 s time to cross a circular ground along its diameter than to cover it once along the boundary. If his speed was 30m/min, than the radius of the circular ground is (take ? = 22/7)
Options- A. 10.5 m
- B. 3.5 m
- C. 5.5 m
- D. 7.5 m Discuss
Correct Answer: 3.5 m
Explanation:
Let the radius of circular field = r m.
Speed of person in m/s = 30/60 = 1/2m/s
According to the question,
[(2?r) /(1/2)] - [(2r)/(1/2)] = 30
? 4?r - 4r = 30
? [4 x (22/7) - 4]r =30
? (125 - 4)r = 30
? (8.5)r = 30
? r = 30/8.5 = 3.5 m
- 5. The area of a rectangular field is 15 time the sum of its length and breadth. If the length of that field is 40 m, what is the breadth of that field?
Options- A. 24 m
- B. 25 m
- C. 28 m
- D. 32 m Discuss
Correct Answer: 24 m
Explanation:
Length ot rectangle = 40 m
Let breadth of = k
Then, according of the question,
(40 + k)15 = 40k
? 600 + 15k = 40k
? 25k = 600
? k = 24 m
- 6. The Different between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is
Options- A. 2520 m2
- B. 2480 m2
- C. 2420 m2
- D. None of these Discuss
Correct Answer: 2520 m2
Explanation:
Let the length of rectangle = L m
? Breadth of rectangle = B m
Using conditions from the question,
L - B = 23 ....(i)
2(L + B) = 206
L + B = 103 ....(ii)
On adding Eqs. (i) and (ii), we get
2L = 126
? L = 63 m
? B = 103 - 63 = 40 m
Then , area of rectangle = L x B
= 63 x 40
= 2520 m2 .
- 7. The area of rectangle whose length is 5 more than twice its width is 75 sq units. What is the perimeter of the rectangle?
Options- A. 40 unit
- B. 30 unit
- C. 24 unit
- D. 20 unit Discuss
Correct Answer: 40 unit
Explanation:
Let the width of the rectangle = k units
? Length = (2k + 5) units.
According to the question,
Area = k(2k + 5)
? 75 = 2k2 + 5k
? 2k2 + 5k - 75 = 0
? 2k2 + 15k - 10k - 75 = 0
? k(2k + 15) - 5(2k + 15) = 0
? (2k + 15) (k - 5) = 0
? k = 5 and -15/2
Width cannot be negative.
? Width = 5 units
? Length = 2x + 5 = 2 x 5 + 5 = 15 unit
? perimeter of the rectangle = 2(15 + 5)
= 40 units
- 8. A rectangle has 30 cm as its length and 720 sq cm as its area. Its area is increased to 1 1/ 4 times its original area by increasing only its length. Its new perimeter is
Options- A. 123 cm
- B. 125 cm
- C. 119 cm
- D. 121 cm Discuss
Correct Answer: 123 cm
Explanation:
Original breadth of rectangle = 720/30 = 24 cm
Now , area of rectangle = (5/4) x 720 = 900 cm2
? New length of rectangle = 900/24 = 37.5 cm
? New perimeter of rectangle = 2(l+ b)
= 2(37.5 + 24 )
= 2 x 61.5
= 123 cm
- 9. The area of a trapezium is 384 sq.cm 2. If its parallel sides are in ratio 3 : 5 and the perpendicular distance between them be 12 cm, The smaller of parallel sides is?
Options- A. 20 cm
- B. 24 cm
- C. 30 cm
- D. 36 cm Discuss
Correct Answer: 24 cm
Explanation:
Let the sides of trapezium be 5k and 3k, respectively
According to the question,
(1/2) x [(5k + 3k) x 12] = 384
? 8k = (384 x 2)/12 = 64
? k = 64/8 = 8 cm
Length of smaller of the parallel sides = 8 x 3 = 24 cm
- 10. The side of a square is 5 cm which is 13 cm less than the diameter of a circle. What is the approximate area of the circle?
Options- A. 245 sq cm
- B. 235 sq cm
- C. 265 sq cm
- D. 255 sq cm Discuss
Correct Answer: 255 sq cm
Explanation:
Diameter of the circle = 13 + 5 = 18 cm
? Radius = Diameter/2 =18/2 = 9 cm
Area of the circle = ?r2 = (22/7) x 92
= (22 x 81)/9
= 1782/7
= 254.57 sq cm
= 255 sq cm
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