aptitude : : mensuration
 
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Important Formulas
  Exercise
   Exercise 2
   Exercise 1
1.
If whole surface area of a sphere is 100π, then its radius will be
 
A.
4.5

B.

7
C.
5
D.
54
   
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Answer: C
Explanation :
        => 4πr2 = 100π
        => r2 = 25
        => r = 5
Radius of the sphere = 5.






 
2.
If whole surface area of a sphere is 100π, then its radius will be
 
A.
4.5

B.

7
C.
5
D.
54
   
  Answer Discuss in Forum Calculator Workspace
Answer: C
Explanation :
        => 4πr2 = 100π
        => r2 = 25
        => r = 5
Radius of the sphere = 5.






 
3.

The circumference of two circles is 88 m and 220 m, respectively. What is the difference between the area of the larger circle and the smaller circle?

 

 
A.

3422 sq m   

B.

3242 sq m   

C.

3244 sq m   

D.

3234 sq m

   
  Answer Discuss in Forum Calculator Workspace
Answer: D
Explanation :

=> 2π = 88 => r = (88*7)/44 = 14 m

Area = πr2 = (22/7)*14*14 = 616 m2  => 2πr1 = 220r1 = ((220*7)/(2*22)) = 35

Area = πr12 = (22/7)*35*35 = 3850m2

Difference 3850-616 = 3234 m2







 
4.
The ratio between the angles of a quadrilateral is 3 : 4 : 6 : 5. Two-third the largest angle of the, quadrilateral is equal to the smaller angle of a parallelogram. What is the value of adjacent angle of the parallelogram?
 
A.
120

B.

110
C.
100
D.
130
   
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Answer: C
Explanation :
=> 3X + 4X + 6X + 5X = 360 => X = 20
Largest angle of quadrilateral = 6X = 6*20 = 120
Smaller angle of parallelogram = 120*(2/3) = 80
So, the adjacent angle = 100






 
5.
What is the area of a circle whose circumference is 132 cm?
 
A.
1562 sq cm

B.

1386 sq cm
C.
180 sq cm
D.
190 sq cm
   
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Answer: B
Explanation :
Circumference of a circle = 132 cm
                                =>  2πr = 132 cm
                  =>  (2*(22/7)*r) = 132 cm
                                      => r = (132*7)/2 => r = 21 cm
Hence, area of a circle = πr2  = (22/7)*21*21 = 1386 sq cm






 
6.
The area of a square is 196 sq cm whose side is half the radius of a circle.The circumference of the circle is equal to breadthof rectangle,if perimeter of the rectangle is 712 cm. What is the length of the rectangle?
 
A.
196 cm

B.

186 cm
C.
180 cm
D.
190 cm
   
  Answer Discuss in Forum Calculator Workspace
Answer: C
Explanation :
Area of square(a)2 = 196 => a = √196 = 14 cm
Radius of a circle = 14*2 = 28 cm
     Circumference = ((22/7)*2*28) = 176 cm
Now, according to question,
                 b = 176 cm
Also,  2(l + b) = 712 => 2(l+176) = 336 => l = 356 -176 => l = 180cm






 
7.
The diagonals of a rhombus are 32 cm and 24 cm  respectively. The perimeter of the rhombus is
 
A.
80 cm

B.

72 cm
C.
68 cm
D.
64 cm
   
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Answer: A
Explanation :

Here, d1 = 32 cm and d2 = 24 cm

Side of rhombus = √(d1/2)2 +(d2/2)2

                               =  √(32/2)2 + (24/2)2

                               =  √256 +144

                               = √400

                               = 20 cm

Perimeter of rhombus  = 4*20 = 80 cm







 
8.
The side of a square is increased by 25%. By what percent does its area increases?
 
A.
25%

B.

45%
C.
56.25%
D.
59.25%
   
  Answer Discuss in Forum Calculator Workspace
Answer: C
Explanation :
We know,
       Change in area = (X+Y+(XY/100))%
                     Here, X = 25 and Y = 25
      Change in area = (25+25+((25*25)/100))%  = (50+6.25)% = 56.25 %






 
9.
The perimeter of square and a circular field are the same. If the area of the circular field is 3850 m2, what is the area of the square?
 
A.
4225 m2

B.

3025 m2
C.
2500 m2
D.
2025 m2
   
  Answer Discuss in Forum Calculator Workspace
Answer: B
Explanation :
Let the radius of the circle be X m.
   π(X)2  =  3850  => X = √(3850*(7/22))  =  √3850*(7/22)  = √35*35  = 35 m
Circumference of circular field = (2*(22/7)*35)m = 220 m
Side of square = (220/4)m = 55 m
So, the area of square = 55*55 m2 = 3025 m2






 
10.
The perimeter of square and a circular field are the same. If the area of the circular field is 3850 m2, what is the area of the square?
 
A.
4225 m2

B.

3025 m2
C.
2500 m2
D.
2025 m2
   
  Answer Discuss in Forum Calculator Workspace
Answer: B
Explanation :
Let the radius of the circle be X m.
   π(X)2  =  3850  => X = √(3850*(7/22))  =  √3850*(7/22)  = √35*35  = 35 m
Circumference of circular field = (2*(22/7)*35)m = 220 m
Side of square = (220/4)m = 55 m
So, the area of square = 55*55 m2 = 3025 m2






 

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