Mensuration Questions for SSC CGL and Bank Exams


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Mensuration Questions for SSC CGL and Bank Exams

 

1. The base of a right prism is a triangle whose perimeter is 28 cm and the in radius of the triangle is 4 cm. If the volume of the prism is 366 cc, then its height is [SSC 10+2-2013]

(a) 4 cm

(b) 8 cm

(c) 6 cm

(d) 6.5 cm

[bg_collapse view="button-green" color="#4a4949" icon="arrow" expand_text="Show Answer " collapse_text="Close Answer " ]

Answer : (d) 6.5 cm

Explanation/Hint :

Given, Perimeter = 28 cm or s = 28/2 = 14 cm

Also, Radius of triangle (r) = 4 cm.

Volume of the prism = 366 cc.

We know, Area of base of prism =

= r x s = 4 x 14 =56 cm2

Volume of prism = Area of base of prism x height of prism

or 366 cc = 56 x h

or h = 6.53 cm

[/bg_collapse]

 

2. The sum of the interior angles of a polygon is 1444°. The number of sides of the polygon is [SSC 10+2-2014]

(a) 6

(b) 9

(c) 10

(d) 12

[bg_collapse view="button-green" color="#4a4949" icon="arrow" expand_text="Show Answer " collapse_text="Close Answer " ]

Answer : (c) 10

Explanation/Hint :

Given, Sum of interior angles of polygon = 10

Sum of interior angles of polygon = (n - 2) x 180°

or n = 10

[/bg_collapse]

 

3. The sides of triangle is given in the ratio of : : and its perimeter is 94 cm. Find the length of largest side of the triangle :

  1. 48 cm 
  2. 42.5 cm
  3. 40 cm 
  4. 47 cm

[bg_collapse view="button-orange" color="#72777c" icon="arrow" expand_text="Show Answer" collapse_text="Close" ]

Answer : c. 40 cm

Explanation/Hint :

Let the sides of triangle be x,
Given sides of triangle : :
= : :L.C.M of 3, 4 ,5)
= 20 : 15: 12 or 20x, 15x and 12x

Now,
20x + 15x + 12x = 94 ( a+b+c = perimeter of triangle )
x = 2, The length of largest side = 20 x 2 = 40 cm

[/bg_collapse]

 

4. The perimeters of two similar triangles ΔABC and ΔPQR are 36 cm and 24 cm respectively. If PQ = 10 cm, the AB is [SSC 10+2-2014]

(a) 15 cm

(b) 12 cm

(c) 14 cm

(d) 26 cm

[bg_collapse view="button-green" color="#4a4949" icon="arrow" expand_text="Show Answer " collapse_text="Close Answer " ]

Answer : (a) 15 cm

Explanation/Hint :

Given, ΔABC ≈ ΔPQR

Thus,  = = =

or =

or =

or =

or AB =15 cm

[/bg_collapse]

 

5. Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is [SSC 10+2-2014]

(a) 1.50 cm

(b) 2.25 cm

(c) 4.50 cm

(d) 9.00

[bg_collapse view="button-green" color="#4a4949" icon="arrow" expand_text="Show Answer " collapse_text="Close Answer " ]

Answer : (c) 4.50 cm

[/bg_collapse]

 

6. If the isosceles right angle triangle has area of 4000 cm 2 the length of its hypotenuse (approx) is :

  1. 25 cm 
  2. 25√20 cm
  3. 40 cm 
  4. 47 cm

[bg_collapse view="button-orange" color="#72777c" icon="arrow" expand_text="Show Answer" collapse_text="Close" ]

Answer : a. 25 cm

Explanation/Hint :

Area of right angle triangle = x base x perpendicular
⇒ 400 = x a2
⇒ a2 = 800 = a = 17.88
Now  h2 = p2 + b2
h2 =  (8√5)2 + (8√5)2
⇒ h = 25.2 (approx) cm
[/bg_collapse]

 

7. The area of right angled triangle is 60 cm 2. If its base is equal to 48 cm . Find its height.

  1. 3 cm 
  2. 4√20 cm
  3. 2 cm
  4. 6cm

[bg_collapse view="button-orange" color="#72777c" icon="arrow" expand_text="Show Answer" collapse_text="Close" ]

Answer : c. 2 cm

Explanation/Hint :

Area of right angle triangle = x base x height
⇒  60 = x 48 x h = 2 cm
[/bg_collapse]

 

8. A triangle with three equal sides has its area equal to 8/3 cm2. Find its perimeter.

  1. 12√2 cm 
  2. 10√2 cm
  3. 12√3 cm 
  4. 9√3  cm

  [bg_collapse view="button-orange" color="#72777c" icon="arrow" expand_text="Show Answer" collapse_text="Close" ]

Answer : a. 12√2 cm

Explanation/Hint :

Area of Equilateral Triangle = a2 cm

⇒ 8√3 = a2

⇒  a2 = 32

⇒  a = 4√2

Perimeter =  3a = 3 x 4 x √2  = 12√2 cm [/bg_collapse]

 

9. Find the area of triangle whose sides measures 10 cm , 12 cm, and 14 cm.

  1. 22√6 cm2
  2. 28√3 cm2
  3. 24√6 cm2
  4. 18√3 cm2

  [bg_collapse view="button-orange" color="#72777c" icon="arrow" expand_text="Show Answer" collapse_text="Close" ]

Answer : c. 24√6 cm2

Explanation/Hint :

Area of Isosceles triangle = , where s =

Here a = 10, b = 12, c = 14

s = = 18 cm

Area = = cm2

[/bg_collapse]

 

10. The base of the triangle is 5 cm and height is 12 cm. The height of another triangle of double the area having the base 20 cm is

  1. 9 cm 
  2. 18 cm
  3. 20 cm 
  4. 12.5 cm

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Answer : b. 18 cm

Explanation/Hint :

x 15 x 12 =   x 20 x h

⇒ h = 18 cm

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11. If the total surface area of a cube is 96 cm2, its volume is [SSC 10+2-2013]

(a) 36 cm3

(b) 56 cm3

(c) 16 cm3

(d) 64 cm3

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Answer : (d) 64 cm3

Explanation/Hint :

Total surface area of cube = 6a2 ..................1

Also, Total surface area of cube = 96 cm2 .............2

From eqn 1 and 2,

6a2 = 96 cm2

or a = 16 cm2

Volume of cube = a3 = 64 cm3

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12. 360 sq. cm and 250 sq. cm are the areas of two similar triangles. If the length of one of the sides of the first triangle be 8 cm, then the length of the corresponding side of the second triangle is [SSC 10+2-2013]

(a) 6 cm

(b) 6 cm

(c) 6 cm

(d) 6 cm

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Answer : (d) 6 cm

Explanation/Hint :

=

or x = 6 cm

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13. The length and breadth of a rectangle are doubled. Percentage increase in area is [SSC 10+2-2013]

(a) 400%

(b) 150%

(c) 200%

(d) 300%

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Answer : (d) 300%

Explanation/Hint :

A = lb

A' = 2L x 2b = 4 lb = 4A

%  Change = =360 %

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14. The difference between the circumference and the radius of a circle is 37 cm. The area of circle is (Take π = [SSC 10+2-2013]

(a) 154 cm2

(b) 259 cm2

(c) 148 cm2

(d) 111 cm2

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Answer : (a) 154 cm2

Explanation/Hint :

Given, circumference - radius of a circle = 37 cm

or 2πr - r = 37 or r = 7

Now, Area of circle = πr2 = 154 cm2

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15. If the sides of a right angled triangle are three consecutive integers, then the length of the smallest side is [SSC 10+2-2014]

(a) 3 units

(b) 2 units

(c) 4 units

(d) 5 units

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Answer : (a) 3 units

Explanation/Hint :

Given, three consecutive integers = 3, 4 and 5

then the length of the smallest side = 3

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16. If the three medians of a triangle are same, then the triangle is [SSC 10+2-2014]

(a) equilateral

(b) isosceles

(c) right-angled

(d) obtuse-angled

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Answer : (a) equilateral

Explanation/Hint :

If the three medians of a triangle are same, then the triangle is equilateral.

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17.Area of a regular hexagon with side 'a' is [SSC 10+2-2014]

(a) sq. unit

(b) sq. unit

(c) sq. unit

(d) sq. unit

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Answer : (c) sq. unit

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18. If the sum of the dimensions of a rectangular parallelepiped is 24 cm and the length of the diagonal is 15 cm, then the total surface area of it is [SSC 10+2-2014]

(a) 420 cm2

(b) 275 cm2

(c) 351 cm2

(d) 378 cm2

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Answer : (c) 351 cm2

Explanation/Hint :

l+b+h = 24

or  =15

or  l2 + b2 + h2= 225

we know, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc

or a2 + b2 + c2 = 2ab + 2ac + 2bc - (a + b + c)2

thus, l2 + b2 + h= (l+b+h)2- 2(lb+bh+lh) = 225

or (l+b+h)2- 2(lb+bh+lh) = 225

or (24)2- 225 = 2(lb+bh+lh)     [ (l+b+h) = 24 given ]

or 2(lb+bh+lh) =Total surface area = 351 cm2

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19. The sides of a triangle are 16 cm, 12 cm and 20 cm. Find the area [SSC 10+2-2013]

(a) 81 cm2

(b) 64 cm2

(c) 112 cm2

(d) 96 cm2

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Answer : (d) 96 cm2

Explanation/Hint :

Given, a = 16, b = 12 and c = 20

Area of Isosceles triangle = , where s =

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