Quantitative Aptitude

Mensuration

2,507 Questions
All Direct Formula Application 1067 Shape Transformations 343 Mensuration Ratio Equations 277 Combined & Hollow Solids 247 Successive Percentage Changes 178 Inscribed & Circumscribed Figures 165 Cost Estimation Problems 100 Liquid Pour & Submergence 67 Unit Conversions 35 Path & Border Calculations 17 Time & Work Integration 7 Scale & Model Proportions 2

Mensuration Questions

Multiple choice

On increasing the radius of a cylinder by 9 units, the volume increases by (p) cubic units. On increasing the altitude of the cylinder by 9 units, the volume also increases by (p) cubic units. If the original altitude is 3 units, what is the original radius?

  1. 3 units

  2. 6 units

  3. 9 units

  4. 12 units

  5. None of These
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cylinder is V = πr²h. When only the radius increases by 9: V₁ = π(r+9)²(3) = 3π(r²+18r+81), so p = 54πr + 243π. When only the height increases by 9: V₂ = πr²(12) = 12πr², so p = 9πr². Setting equal: 54πr + 243π = 9πr². Dividing by 9π: 6r + 27 = r², so r² - 6r - 27 = 0. Factoring: (r-9)(r+3) = 0. Since radius must be positive, r = 9 units.

Multiple choice

If the length of a rectangle is 22m and area of the rectangle is 154m2. Then find the area of the circle whose radius is half of the rectangles breadth?

  1. 37 cm2

  2. 42.5 cm2

  3. 38.5 cm2

  4. 5.5 cm2

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rectangle area = length × breadth, so 154 = 22 × breadth, giving breadth = 7 m = 700 cm. Circle radius = half of breadth = 350 cm. Circle area = pi × r² = (22/7) × 350² = (22/7) × 122500 = 22 × 17500 = 385000 cm² = 38.5 m². Note: The answer options show cm² but the calculation gives 38.5 m² (385000 cm²), which matches option C as 38.5.

Multiple choice

The volume of a cylinder is 2500π cm3 and the radius is 25 cm. The height of the cylinder is equal to the diagonal of a square. Find the area of the square.

  1. 16

  2. 8

  3. 4

  4. 20

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cylinder = πr²h = 2500π. Given r = 25 cm, so π×25²×h = 2500π. 625π×h = 2500π, therefore h = 2500/625 = 4 cm. The height equals the diagonal of a square. For a square with side 's', diagonal = s√2. So s√2 = 4, giving s = 4/√2 = 2√2 cm. Area of square = s² = (2√2)² = 4×2 = 8 cm².

Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. \text{Quantity I:} The area of the rectangle is equal to the area of the square whose side is 24 cm. \text{Quantity II:} The perimeter of the rectangle is 88cm, if the ratio of the length and the breadth of the rectangle is 6 : 5 then the area of rectangle is ?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or the relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Area of square = side^2 = 24^2 = 576 sq cm. Quantity II: Let length = 6x, breadth = 5x. Perimeter = 2(6x + 5x) = 22x = 88, so x = 4. Area = (6*4) × (5*4) = 24 × 20 = 480 sq cm. Since 576 > 480, Quantity I > Quantity II.

Multiple choice

Which information are necessary to answer the questions asked- A metal block of density ‘D’ and mass ‘M’, in the form of a cuboid, is beaten into a thin square sheet of thickness ‘t’, and rolled to form a cylinder of the same thickness. Find the inner radius of the cylinder– Statement I : Cuboid has dimensions 10cm x 5 cm x 12 cm Statement II : Thickness ‘t’ = 1.5cm Statement III : Mass of block, M = 216kg

  1. All three together are not sufficient

  2. All three together are sufficient

  3. I and II together are sufficient

  4. II and (I or III) are sufficient

  5. III or (I and II) are sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives cuboid dimensions (volume = 10×5×12 = 600 cm³). Statement II gives sheet thickness (t = 1.5 cm). From volume and thickness, we can find sheet area = 600/1.5 = 400 cm², then side of square = √400 = 20 cm. When rolled into a cylinder, the square's circumference = 20 cm, so 2πr = 20, giving r = 10/π cm. Mass (Statement III) is irrelevant to the geometry.

Multiple choice

The volume of a right circular cone is equal to the volume of a right circular cylinder. The height and the radius of the cylinder are 9 cm and 20 cm respectively. If the height of the cone is 108 cm, then the radius, in cm, is- लम्ब वृत्ताकार शंकु का आयतन लम्ब वृत्ताकार सिलेंडर के आयतन के बराबर है। सिलेंडर की ऊँचाई और त्रिज्या क्रमशः 9 सेमी. और 20 सेमी. है। यदि शंकु की ऊँचाई 108 सेमी. है, तो उसकी त्रिज्या कितनी (सेमी. में) होगी?

  1. 12

  2. 20

  3. 10

  4. 14
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = πr²h = π × 20² × 9 = 3600π cubic cm. Volume of cone = (1/3)πr²h = (1/3) × π × r² × 108 = 36πr². Setting volumes equal: 36πr² = 3600π, which gives r² = 100, so r = 10 cm. The cone has a smaller radius but greater height to achieve the same volume.

Multiple choice

Calculate the area (in cm2) of a circle whose diameter is 35 cm. एक वृत्त जिसका व्यास 35 सेमी है के क्षेत्रफल (सेमी2 में) की गणना कीजिये।

  1. 1925

  2. 962.5

  3. 857.5

  4. 1715
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a circle is πr² where r is the radius. Given diameter is 35 cm, so radius r = 35/2 = 17.5 cm. Using π = 22/7, Area = (22/7) × (17.5)² = (22/7) × 306.25 = 962.5 cm². Option A is incorrect because it uses diameter instead of radius in calculation. Options C and D are calculation errors.

Multiple choice

Quantity I- the circumference of two circles is 88 meters and 132 meters respectively. What is the difference between the area of larger circle and smaller circle?\ Quantity II- A circle having the area of 616m2. If the circumference of this circle is equal to 200% of the length of the rectangle and width of the rectangle is equal to the perimeter of equilateral triangle with side 6m. What is the area of the rectangle

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: For circumferences 88 m and 132 m, radii are 44/π m and 66/π m. Areas are π × (44/π)² = 1936/π m² and π × (66/π)² = 4356/π m². Difference = (4356 - 1936)/π = 2420/π m². Using π = 22/7: Difference = 2420 × 7/22 = 770 m². Quantity II: Circle area 616 m² gives r = 14 m (using π = 22/7). Circumference = 88 m = 200% of rectangle length, so length = 44 m. Rectangle width = perimeter of triangle (side 6 m) = 18 m. Area = 44 × 18 = 792 m². Comparing: 792 > 770, so Quantity II > Quantity I.

Multiple choice

If the base of the rectangular solid is a square, and the length of the side of the base is 16 cm. and height of the solid is 20 cm. Find the volume of the rectangular solid? यदि किसी आयताकार ठोस का आधार वर्गाकार है, और आधार की भुजा की लम्बाई 16 सेमी है और इसकी ऊंचाई 20 सेमी है तो आयताकार ठोस का आयतन ज्ञात कीजिये ?

  1. 2150 cm2/सेमी 2

  2. 5210 cm2/सेमी 2

  3. 5120 cm2/सेमी 2

  4. 2100 cm2/सेमी 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of rectangular solid = Length × Width × Height. Since base is square with side 16cm: Volume = 16 × 16 × 20 = 256 × 20 = 5120 cm³. Note: Options incorrectly show cm² instead of cm³. Option A (2150) and D (2100) are calculation errors. Option B (5210) reverses digits.

Multiple choice

A cylindrical vessel of radius 6 cm contains water. A solid sphere of radius 9 cm is dipped into the water until it is completely immersed. The water level in the vessel will rise by / 6 सेमी त्रिज्या के बेलनाकार बर्तन में पानी है। 9 सेमी त्रिज्या का एक ठोस क्षेत्र पूरी तरह से डूबने तक पानी में डूब हुआ है। बेलन में जल स्तरकितना बढ़ जाएगा?

  1. 14

  2. 15.5

  3. 18.5

  4. 27
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When the sphere is immersed, the water volume equals the sphere's volume. Sphere volume = (4/3)π(9)³ = 972π cm³. The cylindrical volume rise = π(6)²h = 36πh cm³. Equating: 36πh = 972π, so h = 972/36 = 27 cm. Option D is correct.