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- Question
- 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
- Correct Answer
- 21 m
ExplanationArea 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 - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. A polygon has 44 diagonals the number of its sides is?
Options- A. 9
- B. 10
- C. 11
- D. 12 Discuss
- 9. A square, a circle and equilateral triangle have same perimeter.
Consider the following statements.
I. The area of square is greater than the area of the triangle.
II. The area of circle is less then the area of triangle.
Which of the statement is/are correct?
Options- A. Only I
- B. Only II
- C. Both I and II
- D. Neither I nor II Discuss
- 10. If the area of an equilateral triangle is x and its perimeter is y, then which one of the following is correct?
Options- A. y4 = 432 x2
- B. y4 = 216 x2
- C. y2 = 432 x2
- D. None of these Discuss
Area problems
Search Results
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
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
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%
Correct Answer: 3 cm
Explanation:
? 1/2 x 2 ? x h
= ?3/4 x (2 ?3)2
? h = 3 cm.
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
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
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
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
Correct Answer: Only I
Explanation:
Let the radius of circle is 'r' and a side of a square is 'a',
then given condition
2?r = 4a
? a = ?r/2
? Area of square = (?r/2)2 = ?2 /4r2 = 9.86r2/4 = 2.46r2
and area of circle = ?r2 = 3.14;r2
and let the side of equilateral triangle is x.
Then, given condition,
3x = 2?r
? x = 2?r/3
? Area of equilateral triangle = ?3/4 x 2
= ?3/4 x 4?2r2/9
= ?2/3?3r2
= 1.89r2
Hence, Area of circle > Area of square > Area of equilateral triangle.
Correct Answer: y4 = 432 x2
Explanation:
Area of equilateral triangle = ?3a2/4 = x ......(i)
And perimeter = 3a = y
? a = y/3 ....(ii)
Now, Putting the value of a from Eq. (ii) in Eq. (i). we get
?3 (y/3)2/4 = x
? x = ?3 x y2/36
? x = y2/3?3x = y2/12?3
12?3 x = y2
On squaring both sides, we get
y4 = 432x2
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