Area problems
- 1. If area of a square is 64 sq cm, then find the area of the circle formed by the same perimeter.
Options- A. 215/? sq cm
- B. 216/? sq cm
- C. 256/? sq cm
- D. 318/? sq cm Discuss
Correct Answer: 256/? sq cm
Explanation:
Area of square = 64 sq cm
(Side)2 = 64
? Side = ?64 = 8 cm
According to the question,
? 2?r = 4 x 8
? r = (4 x 8)/2?
? r = 16/?
? Area of the circle
= ? x (16/?) x (16/?) sq cm
= 256/? sq cm.
- 2. The circumference of a circle is 25 cm. Find the side of the square incribed in the circle.
Options- A. 25/??2 cm
- B. 21/??3 cm
- C. 23/??2
- D. 29/??3 cm Discuss
Correct Answer: 25/??2 cm
Explanation:
Circumference of the circle = 2?r = 25
? r = 25 / (2?)
According to the formula,
Side of inscribed square = r?2
= 25 / (2?r x ?2)
= 25 / (??2 ) cm
- 3. The altitude of an equilateral triangle of side 2 ? 3 cm is?
Options- A. ? 3/2 cm
- B. 1/2 cm
- C. ? 3/4
- D. 3 cm Discuss
Correct Answer: 3 cm
Explanation:
? 1/2 x 2 ? x h
= ?3/4 x (2 ?3)2
? h = 3 cm.
- 4. The radius of a circle is increased so that its circumference increase by 5%. The area of the circle will increase by?
Options- A. 10 %
- B. 10.25 %
- C. 8.75 %
- D. 10.5 % Discuss
Correct Answer: 10.25 %
Explanation:
Let circumference = 100 cm .
Then, ? 2?r = 100
? r = 100/2?
=50/?
? New circumference
= 105 cm
Then, 2?R = 105
? R = 105 / (2?)
&rArr Original area = [ ? x (50/?) x (50/?) ]
= 2500/? cm2
? New Area = [? x (105/2?) x (105/2?)]
= 11025 / (4?) cm2
? Increase in area = [11025/(4?)] - 2500/? cm2
= 1025 / 4? cm2
Required increase percent [1025/(4?)] x 2500/? x 100 = 41/4%
= 10.25%
- 5. The length of minute hand of a wall clock is 7 cms. The area swept by minute hand in 30 minutes is?
Options- A. 147 sq. cm
- B. 210 sq. cm
- C. 154 sq. cm
- D. 77 sq. cm Discuss
Correct Answer: 77 sq. cm
Explanation:
Angle swept in 30 min= 180°
Area swept = [(22/7) x 7 x 7] x [180°/360°] cm2
= 77 cm2
- 6. The area of circle inscribed in an equilateral triangle is 462 cm . The perimeter of the triangle is?
Options- A. 42 ? 3 cms
- B. 126 cms
- C. 72.6 cms
- D. 168 cms Discuss
Correct Answer: 126 cms
Explanation:
? 22/7 x r2 = 462
? r2 = (462 x 7) /22 = 147
? r = 7?3 cm
? Height of the triangle = 3r = 21?3 cm
Now, ? a2 = a2/4 + (3r)2
? 3a2/4 = (21?3)2
? a2 = (1323 x 4)/3
? a = 21x 2 = 42 cm
? Perimeter = 3a = 3 x 42
=126 cm
- 7. A park is in the form of a square one of whose sides is 100 m . The area of the park excluding the circular lawn in the centre of the park is 8614 m 2. The radius of the circular lawn is?
Options- A. 21 m
- B. 31 m
- C. 41 m
- D. None of these Discuss
Correct Answer: 21 m
Explanation:
Area of park = 100 x 100 = 10000 m2
Area of circular lawn = Area of park - area of park excluding circular lawn
= 10000 - 8614
= 1386
Now again area of circular lawn = (22/7) x r2 = 1386 m2
? r2 = (1386 x 7) / 22
= 63 x 7
= 3 x 3 x 7 x 7
? r = 21 m
- 8. A room 5.44 m x 3.75 m is to be paved with square tiles. the least number of tiles required to cover the floor is?
Options- A. 162
- B. 176
- C. 184
- D. 192 Discuss
Correct Answer: 176
Explanation:
Area of the room =(544 x 374) cm2
size of largest square tile = H.C.F. of 544 & 374
= 34 cm
Area of 1 tile = (34 x 34) cm2
? Least number of tiles required
= (544 x 374) / (34 x 34) = 176
- 9. The ratio of the corresponding sides of two similar triangles is 3 : 4, The ratio of their areas is?
Options- A. 4 : 3
- B. 3 : 4
- C. 9 : 16
- D. ? 3: 2 Discuss
Correct Answer: 9 : 16
Explanation:
Ratio of similar triangle
= Ratio of the square of corresponding sides
= (3x)2 / (4x)2 = 9x2 / 16x2
= 9/16 = 9 : 16
- 10. A polygon has 44 diagonals the number of its sides is?
Options- A. 9
- B. 10
- C. 11
- D. 12 Also asked in: Bank Exams
Correct Answer: 11
Explanation:
Let there be n sides of the polygon. Then it has n vertices.
The total number of straight lines obtained by joining n vertices by talking 2 at a time is nC2
These nC2 lines also include n sides of polygon.
Therefore, the number of diagonals formed is nC2 - n.
Thus, nC2 - n = 44
? [n(n - 1)/2] - n = 44
? ( n2 - 3n) / 2 = 44
? n2 - 3n = 88
? n2 - 3n - 88 = 0
?(n - 11) (n + 8) = 0
? n = 11
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