# Mensuration Questions and Answers updated daily – Aptitude

Mensuration Questions: Solved 782 Mensuration Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

## Mensuration Questions

101. The radius of a circle is two fifth of that of a sphere. The volume of the sphere is 32000Ï€/3 m

^{3}. If ratio between area of a square and that of the circle is 14 : 11, then what is the perimeter of the square (Use Ï€ = 22/7)SHOW ANSWER

Correct Ans:64 m

Explanation:

Volume of sphere = (4/3) â„¼ r

(4/3) â„¼ r

r

r

Therefore, radius of circle = (â…–)*20 = 8 m

Given that,

Area of square/Area of circle = 14/11

a

a

a

a

a = 16 m

Perimeter of square = 4a = 4*16 = 64 m

^{3}(4/3) â„¼ r

^{3}= (32000 â„¼)/3r

^{3}= 8000r

^{3}= 20 mTherefore, radius of circle = (â…–)*20 = 8 m

Given that,

Area of square/Area of circle = 14/11

a

^{2}/(â„¼r^{2}) = 14/11a

^{2}/(â„¼*64) = 14/11a

^{2}= (14*64*22)/(11*7)a

^{2}= 256 ma = 16 m

Perimeter of square = 4a = 4*16 = 64 m

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

SHOW ANSWER

Correct Ans:180 cm

Explanation:

Given, Area of a square = 196 sq cm

W.K.T:

=> (side)^2 = 196

=> side = sqrt(196)

=>

Given, side of square = (1/2) of radius of circle

=> 14 = r/2

=> r = 14 * 2

=>

= 2 * (22/7) * 28

= 2 * 22 * 4

= 176

Given,

=>

Given,

=> 2(l + b) = 712

=> 2(l + 176) = 712

=> (l + 176) = 712 / 2

=> l + 176 = 356

=> l = 356 - 176

=>

Thus,

W.K.T:

**Area of square**=**(side)^2**=> (side)^2 = 196

=> side = sqrt(196)

=>

**side of square**=**14 cm**Given, side of square = (1/2) of radius of circle

=> 14 = r/2

=> r = 14 * 2

=>

**r = 28 cm****Circumference of circle = 2 * pi * r**= 2 * (22/7) * 28

= 2 * 22 * 4

= 176

Given,

**Circumference of circle**=**breadth of rectangle**=>

**b = 176 cm**Given,

**Perimeter of rectangle**= 712=> 2(l + b) = 712

=> 2(l + 176) = 712

=> (l + 176) = 712 / 2

=> l + 176 = 356

=> l = 356 - 176

=>

**l = 180 cm**Thus,

**the length of the rectangle = 180 cm**
Workspace

103. The base of a parallelogram is 36 units and the area of the isosceles triangle constructed on the same base between the parallel lines of the parallelogram is 378 square units. Then the vertical distance between the parallel lines is:

SHOW ANSWER

Correct Ans:21

Explanation:

Given

Base of the parallelogram = Base of the isosceles triangle = 36 units.

And the isosceles triangle is constructed between the parallel lines of the parallelogram.

Then, the altitude of that triangle becomes the vertical distance between the parallel lines (ie., Height of parallelogram).

i.e., we have to find the altitude of that triangle

Given, Area of isosceles triangle = 378 sq.units

=> 1/2 x base x height = 378

=> 1/2 x 36 x height = 378

=>

=> height = 378 / 18

=> height =

The vertical distance between the parallel lines = Height =

Base of the parallelogram = Base of the isosceles triangle = 36 units.

And the isosceles triangle is constructed between the parallel lines of the parallelogram.

Then, the altitude of that triangle becomes the vertical distance between the parallel lines (ie., Height of parallelogram).

i.e., we have to find the altitude of that triangle

Given, Area of isosceles triangle = 378 sq.units

**W.K.T: Formula for Area of the triangle = 1/2 x base x height**=> 1/2 x base x height = 378

=> 1/2 x 36 x height = 378

=>

**height**= 378 * 2 / 36=> height = 378 / 18

=> height =

**21**The vertical distance between the parallel lines = Height =

**21 units**.
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104. If the area of the circle and the circumference of the circle are numerically equal, find the radius of the circle?

SHOW ANSWER

Correct Ans:2

Explanation:

**Area of the circle = pi * r^2**

**Circumference of the circle = 2 * pi * r**

Given, Area of the circle = Circumference of the circle

=> pi * r^2 = 2 * pi * r

=>

**r = 2**

**Thus, radius = 2 units**

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105. Find the area between the concentric circles whose radius are 10 and 9 respectively.

SHOW ANSWER

Correct Ans:19 pi

Explanation:

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106. Find the area of the concentric circle whose radius are 12 m and 10 m respectively?

SHOW ANSWER

Correct Ans:44 pi

Explanation:

W.K.T: Concentric circlesarecircleswith a common center.

Given, radius of larger circle = 12 m

radius of smaller circle = 10 m

Area of larger circle = pi * (12)^2 = 144 pi

Area of smaller circle = pi * (10)^2 = 100 pi

Given, radius of larger circle = 12 m

radius of smaller circle = 10 m

**Area of circle = pi * r^2**Area of larger circle = pi * (12)^2 = 144 pi

Area of smaller circle = pi * (10)^2 = 100 pi

**Area between the these two concentric circles = 144 pi – 100 pi****= 44 pi**
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107. Find the volume of the cuboid of side 2 m x 3 m x 4 m

SHOW ANSWER

Correct Ans:24 m^3

Explanation:

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108. Find the slant height of the cone of radius 24 and height 7 cm ?

SHOW ANSWER

Correct Ans:25

Explanation:

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109. If a right circular cone of height 24 cm has a volume of 1232 cm cube, then the area of its curved surface is :

SHOW ANSWER

Correct Ans:550

Explanation:

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110. The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km square. The height of mountain is

SHOW ANSWER

Correct Ans:2.4

Explanation:

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111. The radii of two cones are in ratio 2:1, their volumes are equal. Find the ratio of their heights.

SHOW ANSWER

Correct Ans:(1 : 4)

Explanation:

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112. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

SHOW ANSWER

Correct Ans:12 pi

Explanation:

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113. The volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is:

SHOW ANSWER

Correct Ans:89.8

Explanation:

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114. 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. Find the diameter of each sphere.

SHOW ANSWER

Correct Ans:4

Explanation:

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115. Find the sum of the volume of two spheres of radius each 1 unit.

SHOW ANSWER

Correct Ans:8.38

Explanation:

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116. Find the surface area of the sphere of radius 30 (rounded it to the nearest value)

SHOW ANSWER

Correct Ans:11304

Explanation:

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117. A sphere of radius 10 cm is given, find the volume.

SHOW ANSWER

Correct Ans:4190.5

Explanation:

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118. A solid spherical ball of radius 4cm is melted to form spheres of radius 2cm each. The number of spheres so formed is

SHOW ANSWER

Correct Ans:8

Explanation:

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119. The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.

SHOW ANSWER

Correct Ans:704

Explanation:

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120. Find the volume of the hemisphere of radius 2 cm.

SHOW ANSWER

Correct Ans:16.76

Explanation:

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