Mensuration Questions with solution for Competitive Exams. Latest, new questions from SSC CGL, CHSL previous year exam question paper.

### Mensuration Questions : free online practice for Competitive Exams

**Q.1:** What is the perimeter (in cm) of an equilateral triangle whose height is 3.46 cm ?Take .

(A) 12

(B) 9

(C) 6

(D) 10.4**(SSC CHSL August 2021)**

###### Show Answer

height of equilateral side

a = 3.46

a = 3.46

a = 2 x 2 = 4

Peimeter = 3a = 4 x 3 = 12

**Q.2:** The perimeters of two similar triangles ABC and PQR are 156 cm and 46.8 cm respectively. If BC = 19.5 cm and QR = x cm, then the value of x is:

(A) 3.76 cm

(B) 5.85 cm

(C) 4.29 cm

(D) 6.75 cm

**(SSC CHSL August 2021)**

###### Show Answer

=

5.85 cm

**Q.3:** The radius of a sphere is 9 cm. It is melted and drawn into a wire of radius 0.3 cm. The length of the wire is:

(A) 112 m

(B) 108 m

(C) 118 m

(D) 106 m

**(SSC CHSL August 2021)**

###### Show Answer

Volume of sphere = Wire volume

= r

^{2}h

= x 0.3 x 0.3 x h

h =

h = 10800 cm = 108 m

**Q.4:** One side of a rectangular field is 39 m and its diagonal is 89 m. What is the area of the field ?

(A) 3120 m^{2}

(B) 2100 m^{2}

(C) 2160 m^{2}

(D) 3140 m^{2}

**(SSC CHSL August 2021)**

###### Show Answer

^{2}

Side = 39

Diagonal = 89

Second side

Second Side =80

Area of field = First Side x Second side (l x b)

= 80 x 39 = 3120 m

^{2}

**Q.5:** The base of a triangle to the perimeter fo a square whose diagonal is cm and its height is equal to the side of square whose area is 169 cm^{2} . The area (in cm^{2} ) of the triangle is:

(A) 130

(B) 182

(C) 175

(D) 156

**(SSC CHSL August 2021)**

###### Show Answer

Diagonal of square

=

a = 7

Perimeter of Square = 4a = 28

Perimeter of square = Base of Triangle = 28

Area of Square = 169

Side of Square = 13

Height of Triangle = Side of square = 13

Area of Triangle = x b x h

= =182

**Q.6:** If the adjacent sides of a rectangle whose perimeter is 60 cm are in the ratio 3 : 2, then what will be the area of the rectangle ?

(A) 864 cm^{2}

(B) 216 cm^{2}

(C) 60 cm^{2}

(D) 300 cm^{2}

**(SSC CHSL August 2021)**

###### Show Answer

^{2}

Ration of side = 3 : 2

Perimeter = 60

Perimeter of rectangle = 2 ( l + b)

2(3n + 2n) = 60

5n = 30, n = 6

l = 3n = 3 x 6 = 18

b = 2n = 2 x 6 = 12

Area = l x b = 18 x 12 = 216 cm

^{2}

**Q.7:** The perimeter of a right angle triangle whose sides that make right angles are 15 cm and 20 cm is:

(A) 60 cm

(B) 40 cm

(C) 70 cm

(D) 50 cm

**(SSC CHSL August 2021)**

###### Show Answer

Diagonal of Right angle triangle

(Third Side )

Diagonal = 25

Perimeter = Sum of all sides = 15 + 20 + 25= 60 cm

**Q.8:** The difference between the two perpendicular sides of a right-angled triangle is 17 cm and its area is 84 cm^{2} . What is the perimeter (in cm ) of the triangle ?

(A) 65

(B) 49

(C) 72

(D) 56

**(SSC CHSL August 2021)**

###### Show Answer

b – h = 17

Area = x b x h = 84

b x h = 168 = 24 x 7

b = 24

h = 7

Diagonal

^{2}= b

^{2}+ h

^{2}= 24

^{2}+ 7

^{2}

=> 576 + 49 = 625

Diagonal= 25

Sides of Triangle= 7, 24, 25

Perimeter = 7 + 24 + 25 = 56

**Q.9:** A solid metallic sphere of radius 10 cm is melted and recast into spheres of radius 2 cm each. How many such spheres can be made ?

(A) 64

(B) 216

(C) 125

(D) 100

**(SSC CHSL August 2021)**

###### Show Answer

Volume of big sphere = n x Volume of small sphere

V =

= n x

10 x 10 x 10 = n x 2 x 2x 2

1000 = n x 8

n = 125

**Q.10:** The sum of the squares of the sides of a rhombus is 1600 cm^{2} . What is the side of the rhombus ?

(A) 10 cm

(B) 15 cm

(C) 20 cm

(D) 25 cm

**(SSC CHSL August 2021)**

###### Show Answer

All the sides of rhombus are equal

The sum of the squares of sides = 1600

a

^{2}+ a

^{2}+ a

^{2}+ a

^{2}= 1600

4a

^{2}= 1600

a

^{2}= 400

a = 20

Mensuration Questions for Competitive Exams

**Q.11:** The volume of a right circular cone is 462 cm^{3} . If its height is 12 cm, then the area of its base (in cm^{2} ) is:

(A) 124.5

(B) 103.5

(C) 115.5

(D) 98.5

**(SSC CHSL August 2021)**

###### Show Answer

Volume of Cone =

= 462

r

^{2}=

=

r

^{2}=

Area of base =

=

= 115.5

**Q.12:** How many bricks each measuring 64 cm x 11.25 cm x 6 cm. will be needed to build a wall measuring 8m x 3m x 22.5m ?

(A) 200000

(B) 250000

(C) 67500

(D) 125000

**(SSC CHSL August 2021)**

###### Show Answer

Volume of wall = V1

Volume of Brick= V2

Number of Bricks =

=

=

= 125000

**Q.13:** If the radius of a circle is equal to a diagonal of a square whose area is 12 cm^{2} , then the area of the circle is:

(A) 28 cm^{2}

(B) 36 cm^{2}

(C) 32 cm^{2}

(D) 24 cm^{2}

**(SSC CHSL August 2021)**

###### Show Answer

^{2}

Area of Square = 12

Side of Square =

Diagonal of square= side x

=

Radius of Circle = Diagonal of Square

=

Area of circle =

=

=24

**Q.14:** The sum of three sides of an isosceles triangle is 20 cm, and the ratio of an equal side to the base is 3 : 4, The altitude of the triangle is:

(A) cm

(B) cm

(C) cm

(D) cm

**(SSC CHSL August 2021)**

###### Show Answer

Ration of side and base = 3 : 4

Sides 3x, 3x, 4x

Sum of sides = 20

3x + 3x + 4x = 20

10x = 20

x = 2

Sides = 6, 6, 8

Height =

= 36 – 16

=

=

**Q.15:** If the volume of a sphere is cm^{3} , then its radius is:

(A) 5 cm

(B) 6 cm

(C) 4.5 cm

(D) 5.5 cm

**(SSC CHSL August 2021)**

###### Show Answer

Volume of Sphere =

=

r

^{3}=

r

^{3}=

r =

= 5.5 cm

**Q.16:** The area of the largest that can be inscribed in a semi-circle of radius 6 cm is:

(A) 38cm^{2}

(B) 35cm^{2}

(C) 36cm^{2}

(D) 34cm^{2}

**(SSC CHSL August 2021)**

###### Show Answer

^{2}

Base of Tringle = Diameter of semi-circle

Base of Triangle = 12

Height of Triangle = radius of semi-circle

Height= 6

Area of Triangle= x base x height

= x 12 x 6 = 36 cm

^{2}

**Q.17:** A solid metallic sphere of radius 12cm is melted and recast in the form of small spheres of radius 2 cm. How many small spheres are formed ?

(A) 96

(B) 864

(C) 216

(D) 24

**(SSC CHSL August 2021)**

###### Show Answer

Volume of Big sphere= V1

Volume of small sphere= V2

Number of Spheres =

=

=

= 6 x 6 x 6 = 216

**Q.18:** The square of the diagonal of a cube is 2175 cm^{2} . What is the total surface area (in cm^{2} ) of the cube ?

(A) 4272

(B) 4305

(C) 4350

(D) 4530

**(SSC CHSL August 2021)**

###### Show Answer

Diagonal of square =

= 2175

a

^{2}=

a

^{2}= 725

total surface area = 6a

^{2}

= 6 x 725 = 4350

**Q.19:** A rectangle with perimeter 50 cm has its sides in the ratio 1 : 4. What is the perimeter of a square whose area is the same as that of the rectangle ?

(A) 45 cm

(B) 36 cm

(C) 50 cm

(D) 40 cm

**(SSC CHSL August 2021)**

###### Show Answer

Let sides are x , 4x

Perimeter = 2(l + b)

2(x + 4x) = 50

5x = 25, x = 5

Length= 20 cm

Breath= 5 cm

Area= l x b = 20 x 5 = 100

As per question, Area of Rectangle = Area of Square

a

^{2}= 100, a = 10

Perimeter of square= 4 x side = 4 x 10 = 40

**Q.20:** The inner and outer radius of two concentric are 6.7 cm and 9.5 cm, respectively. What is the difference between their circumferences (in cm ) ?

(A) 10.4

(B) 17.6

(C) 6.5

(D) 20.5

**(SSC CHSL August 2021)**

###### Show Answer

Circumference of circle =r

Difference of Circumference

=R – r

= [ 9.5 – 6.7]

=

= 17.6

Thanks for attempt Mensuration Questions for Competitive Exams

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