Maths Mensuration Questions Answers With Hindi Explanation

Maths Mensuration Questions Answers  With Hindi Explanation

Maths Mensuration Questions Answers  With Hindi Explanation

Q1.There is a pyramid on a base which is a regular hexagon of side 2a cm. If every slant edge of this pyramid is of length  5a/2 cm, then the volume of this pyramid is

(a) 3a³ cm³

(b) 3 √2a³ cm³

(c) 3√3a³ cm³

(d) 6a³ cm³

Option: (c)

Explaination :

Area of the base =6×√3/4 ×(2a)² =6×√3/4 ×4a²=6√3a² sq.cm

Height

Volume of pyramid=1/3× area of the base × height=1/3×6√3a² ×3/2 a=3√3a³  cm³

Q2.The length of a diagonal of a square is 15√2 cm. Its area is

(a) 112.5 cm²

(b) 450 cm²

(c)  225√2/2 cm²                    

(d) 225 cm²

Option: (d)

Explaination :Diagonal of square = √2×side

√2×side=15√2

⇒side=15√2 /√2=15

Area of square =15×15=225sq.cm 

Q3.The respective heights and volumes of a hemisphere and a right circular cylinder are equal, then the ratio of their radii is:

(a)√2  : √3

(b)√3  : 1

(c)√3 : √2

(d) 2 :√3

Option: (c)

Explaination :

Radius of hemisphere = height of cylinder = r units

Q4.A toy is in the form of a cone mounted on a hemisphere. The radius of the hemisphere and that of the cone is 3 cm and height of the cone is 4 cm. The total surface area of the toy is

(a) 75.43 sq cm

(b) 103.71 sq cm

(c) 85.35 sq cm

(d) 120.71 sq cm

Option: (b)

Explaination :

Total surface area of the toy =πrl+πr²

Q5. At each corner of a triangular field of sides 26m, 28m and 30m, a cow is tethered by a rope of length 7m. The area (in m²) ungrazed by the cows is:

(a) 366

(b) 259

(c) 154

(d) 77

Option: (b)

Explaination :Area grazed by all cows = 180º/360º πr²

πr² /2  =1/2×22/7×7×7  =77 sq.meter

Semi-perimeter of triangular field(s) =26+28+30/2 =42 meter

Area of the field =

Area ungrazed by the cows = 336 – 77 = 259sq.metre

Q6.The volumes of two spheres are in the ratio 8 : 27. The ratio of their surface areas is:

(a) 4 : 9

(b) 2 : 3

(c) 4 : 5

(d) 5 : 6

Option: (a)

Explaination :

Let the volumes be 8x³ and 27x³ 

Their radius are 2x and 3x

The ratio of their surface area= 4x² : 9x² =4 :9

Q7.The height of the cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is  1/27 of the volume of the cone, at what height, above the base, is the section made?

(a) 6 cm

(b) 8 cm

(c) 10 cm

(d) 20 cm

Option: (d)

Explaination :Let H and R be the height and radius of bigger cone respectively and h and r that of smaller cone.

From triangles AOB and AMN, A is common and MN ? OB.   Triangles AOB and AMN are similar,

so AO/AM =BO/MN

⇒30/h=R/r..............(i)

Volume of smaller cone =1/3πr²h

Volume of bigger cone =1/3πR²H

According to the question, 1/3πr²h=(1/3πR²H)×1/27

⇒r²h=R²H/27

27r²h=R²H

27h/H =R²/r²

27h/H =(30/h)²

27h/H =900/h²⇒ 27h³=900H=900×30

h³=900×30/27 =1000

h=10cm

Required height = 30 – 10 = 20 cm

Q8.A sphere and a cylinder have equal volume and equal radius. The ratio of the curved surface area of the cylinder to that of the sphere is:

(a) 4 : 3

(b) 2 : 3

(c) 3 : 2

(d) 3 : 4

Option: (b)

Explaination :

Q9.The diameter of the base of a right circular cone is 4 cm and its height 2√3 cm. The slant height of the cone is:

(a) 5 cm

(b) 4 cm

(c) 2√3 cm

(d) 3 cm

Option: (b)

Explaination :Slant height of cone

Q10.The ratio of the length of the parallel sides of a trapezium is 3 : 2. The shortest distance between them is 15 cm. if the area of the trapezium is 450 cm², the sum of the lengths of the parallel sides is:

(a) 15 cm

(b) 36 cm

(c) 42 cm

(d) 60 cm

Option: (d)

Explaination :Area of the trapezium = 1/2 (Sum of parallel sides)×altitude

450=1/2(3x+2x)×15

5x=450×2/15

=60cm

Q11.An equilateral triangle and a regular hexagon have the same perimeter. The ratio of the area of the triangle to that of the hexagon is:

(a) 3 : 2

(b) 2 : 3

(c) 1 : 2

(d) 1 : 4

Option: (b)

Explaination :

If the side of an equilateral triangle be x units and side of regular hexagon be y units,

then 3x=6y  ⇒x/y=2

√3/4x² /6×√3/4 y²  

1/6×4=2/3 ;

2:3

Q12.In measuring the sides of a rectangle, there is an excess of 5% on one side and 2% deficit on the other. Then the error percent in the area is:

(a) 3.3

(b) 3.0

(c) 2.9

(d) 2.7

Option: (c)

Explaination :Required percentage =  (x+y+xy/100)%

Negative sign for decrease =(5-2-10/100)%=2.9%

Q13.A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of the cube is:

(a) √π:√6

(b) √6:√π

(c)  √2 :√π

(d)√π:√3

Option: (b)

Explaination :

If the radius of the sphere be r units and the edge of the cube be x units, then

Surface area of sphere = Surface area of cube ⇒ 4πr²=6x²

r²/x² =6/4π

3/2π;   r/x=√3/√2π

Q14.A circle and a square have equal areas. The ratio of a side of the square and the radius of the circle is

(a) 1 : √π

(b)  √π:1

(c) 1 :π

(d) π : 1

Option: (b)

Explaination :

If the radius of circle be r units and the side of square be x units,

then   X² =πr²

⇒x²/r²=π/1

x/r=√π/1

Q15.Surface areas of three adjacent faces of a cuboid are p, q, r. its volume is

(a)

(b) 

(c)   

(d)(√pqr)

Option: (d)

Explaination :

If the length, breadth and height of a cuboid be t, b and h units respectively,

then P = lb,  q = bh, r = hl

pqr=l²b²h²

Volume of the cuboid = lbh =√pqr

Q16.A copper wire, when bent in  the  form of a square  encloses  a  region  having  area 121 cm². If the same wire is bent in the form of a circle,  the area of the region enclosed by the wire will be [π = 22/7]

(a) 154 cm²

(b) 143 cm²

(c) 132 cm²

(d) 121 cm²

Option: (a)

Explaination :Side of a square = √area =√121=11cm

Length of wire = Perimeter of square= 4 ×11=44cm

Circumference of circle =2rπ

2rπ=44

r=7cm

Area of circle-πr²=22/7×7×7 =154 cm²

Q17.A solid cone of height 9 cm with diameter of its base 18 cm is cut out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is:

(a) 25

(b) 30

(c) 50

(d) 75

Option: (d)

Explaination :Volume of sphere =

4/3 πr³ =4/3π ×9×9×9 =972π cu. cm.

Volume of cone =1/3πR²H

1/3π ×9×9×9 =243πcu.cm.

Percentage of wood wasted =(972π-243π)/972π  ×100

=75%

Q18.The area of an equilateral triangle is 4√3 cm². The length of each side of the triangle is:

(a) 3 cm

(b) 2√2 cm

(c) 2√3  cm

(d) 4 cm

Option: (d)

Explaination :Area of the equilateral triangle = √3/4 ×side²

4√3=√3/4 ×side²

side²=4√3×4/√3 =16

side=√16=4cm

Q19.The radius of a circle is increased by 1%. How much does the area of the circle increase?

(a) 1%

(b) 1.1%

(c) 2%

(d) 2.01%

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Option: (d)

Explaination :Effect on area = (1+1+11/100)% =2.01%

Q20.The circumference of a circle is 100 cm. The measure of a side of the square inscribed in this circle is

(a) 25√2πcm

(b) 50√2/π cm

(c) 50√2π cm

(d) 25√2/π cm

Option: (b)

Explaination :Circumference of the circle = π×Diameter=100

d=100/π   cm

Q21.In a cylindrical vessel of diameter 24 cm filled up with sufficient quantity of water, a solid spherical ball of radius 6 cm is completely immersed.The increase in height of water level is:

(a) 1.5 cm

(b) 2 cm

(c) 3 cm

(d) 4.2 cm

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Option: (b)

Explaination :If the height of increased water level be h cm, then

πr²h=4/3 πR³

12×12×h=4/3×6×6×6

h=2 cm

Q22.A cow is tied on the corner of a rectangular field of size 30m  ×20m by a 14m long rope. The area of the region, that she can graze, is :(π = 22/7)

(a) 350 m²

(b) 196 m²

(c) 154 m²

(d) 22 m²

Option: (c)

Explaination :area of the region, that cow can graze

90/360 π r²

90/360 ×22/7 ×14×14 =154 sq.meter

Q23.The diameters of two cylinders, whose volumes are equal, are in the ratio 3 : 2. Their heights will be in the ratio:

(a) 4 : 9

(b) 5 : 6

(c) 5 : 8

(d) 8 : 9

Option: (a)

Explaination :

Q24.A 7 m wide road runs outside around a circular park, whose circumference is 176 m. The area of the road is: [π = 22/7]

(a) 1386 m²

(b) 1472 m²

(c) 1512 m²

(d) 1760 m²

Option: (a)

Explaination :

If the radius of the circular park be r metre, then,

2πr=176

2×22/7×r=176

r=28 meter

Radius of the park with road = 28 + 7 = 35 metre

Area of the road =22/7(35²-28²)=22/7×63×7=1386 meter² 

Q25.A cube and a sphere have equal surface areas. The ratio of their volumes is:

(a) π : 6

(b) √π :  √6

(c) √6 : √π

(d) 6 :π

Option: (b)

Explaination :

Surface area of cube = 6?² ;

Surface area of sphere = 4πr² ;

6?² = 4πr²

⇒l/r=2√π/√6