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

A sphere has a radius of 5 cm. If it is divided into two hemispheres, what would be the total surface area of the two hemispheres?
  1. $75 π cm2$
  2. $125 π cm2$
  3. $150 π cm2$
  4. $100 π cm2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A sphere has surface area 4πr². When divided into two hemispheres, each hemisphere has curved surface area 2πr² plus circular base area πr², giving total 3πr² per hemisphere. For two hemispheres: 2×3πr² = 6πr² = 6π(5)² = 150π cm². Option B (125π) incorrectly uses 5πr² formula, and options A and D don't match the correct calculation.

Multiple choice

Sum of the circumference of two circles is 220 cm. If the ratio between the radius of these two circles is 2 : 3 then find the sum of area of bigger circle and a square whose side is two times of the radius of smaller circle?

  1. 2140 cm2

  2. 2150 cm2

  3. 2170 cm2

  4. 2155 cm2

  5. 2175 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the radii be 2r and 3r (given ratio 2:3). Circumference = 2πR, so 2π(2r) + 2π(3r) = 220. This gives 10πr = 220, so r = 7 (using π = 22/7). Larger circle radius = 21 cm, area = π(21)² = 1386 cm². Square side = 2 × smaller radius = 2 × 14 = 28 cm. Square area = 784 cm². Total area = 1386 + 784 = 2170 cm².

Multiple choice

A container is formed by surmounting a hemisphere on a right circular cylinder of same radius as that of hemisphere. If the volume of the container is (576\pi) m3 and radius of cylinder is 6m, then find the height of the container.

  1. 14 m

  2. 12 m

  3. 20 m

  4. 18 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total volume = cylinder volume + hemisphere volume. Hemisphere volume = (2/3)πr³ = (2/3)π(6)³ = 144π m³. Cylinder volume = 576π - 144π = 432π m³. Using V = πr²h, we get π(6)²h = 432π, so h = 12 m. Total height = cylinder height + hemisphere height = 12 + 6 = 18 m.

Multiple choice

The height of the right circular cone is 5 cm and its base radius is 12 cm. What is curved surface area of the cone ?

  1. 132πcm2

  2. 143 πcm2

  3. 156 πcm2

  4. 168 πcm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a right circular cone with height h = 5 cm and base radius r = 12 cm, first find the slant height l using Pythagoras theorem: l = √(h² + r²) = √(25 + 144) = √169 = 13 cm. The curved surface area is πrl = π × 12 × 13 = 156π cm². Option A incorrectly uses l = 11, giving 132π. Option B uses incorrect dimensions.

Multiple choice

Tiles of (1.5 \times 2) meter dimension in the rectangular hall of (20 \times 15) meter square have been laid. 20% of the total tiles are blue, remaining 30% tiles are of yellow color and rest of the 50% tiles are of red color and the remaining tiles are white. What is the area covered by white tiles?
  1. $56 m2$
  2. $60 m2$
  3. $120 m2$
  4. $84 m2$

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

Hall area = 20 × 15 = 300 m². Each tile = 1.5 × 2 = 3 m². Total tiles = 300/3 = 100. Blue tiles = 20% of 100 = 20. Yellow tiles = 30% of remaining 80 = 24. Red tiles = 50% of remaining 56 = 28. White tiles = remaining = 56 - 28 = 28. White tile area = 28 × 3 = 84 m², which is option D.

Multiple choice

A hemispherical bowl of internal diameter 78 cm contains a liquid. The liquid is to be filled in conical bottles of radius 13 cm and height 3 cm . Then find the number of bottles that can be filled .

  1. 234

  2. 243

  3. 432

  4. 324

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

Volume of hemisphere = (2/3)πr³ = (2/3)π(39)³ = 39462π cm³. Volume of one cone = (1/3)πr²h = (1/3)π(13)²(3) = 169π cm³. Number of bottles = 39462π/169π = 233.5, which rounds to 234 complete bottles. The key is equating total volume and computing the ratio.

Multiple choice

The ratio between the curved surface area and the total surface area is 2:3 and the total surface area is 924 cm2. What is the volume of the cylinder?(in cm3)

  1. 2156

  2. 2183

  3. 2492

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

CSA: TSA = 2:3, so CSA = (2/3)×924 = 616. For cylinder: TSA = 2πr(r+h) = 924, CSA = 2πrh = 616. Dividing: h/(r+h) = 616/924 = 2/3, so 3h = 2r + 2h, giving h = 2r. From 2πr(3r) = 924, r = 7, h = 14. Volume = πr²h = π×49×14 = 2156.

Multiple choice

What is the cost of flooring of a rectangular hall? I. Length of the rectangle is 6 meter. II. Breadth of the rectangle is two-third of its length. III. Cost of flooring the area of 100 (cm^2) is Rs 45.

  1. I and III

  2. II and III

  3. All I, II and III

  4. Can’t be answered using all the above statements.

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

From I: Length = 6m. From II: Breadth = (2/3)*6 = 4m. Area = 6*4 = 24m² = 240000 cm². From III: Cost of 100 cm² = Rs 45, so cost per cm² = Rs 0.45. Total cost = 240000 * 0.45 = Rs 108000. All three statements are needed: I and II give dimensions, III gives rate. Without any one, the answer cannot be determined.

Multiple choice

In the following questions, two quantities are given as Quantity I and Quantity II. Find the correct relationship. $The perimeter of a square is equal to twice the perimeter of a rectangle of length 11 cm & breadth 10 cm \text{ Quantity I: } Find the circumference of a semicircle whose diameter is equal to the side of the square. \text{ Quantity II: } Find the circumference of another semicircle whose radius is 14 cm$

  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

Rectangle perimeter = 2(11+10) = 42 cm. Square perimeter = 2 × 42 = 84 cm, so side = 21 cm. Quantity I: Semicircle with diameter 21 cm has radius 10.5 cm. Circumference of semicircle = πr + 2r = (π × 10.5) + 21 ≈ 33 + 21 = 54 cm. Quantity II: Semicircle with radius 14 cm has circumference = πr + 2r = (π × 14) + 28 ≈ 44 + 28 = 72 cm. Clearly 72 > 54, so Quantity II exceeds Quantity I.

Multiple choice

The base of the right prism is a triangular with sides 20 cm, 21 cm and 29 cm, If its volume is 7560 cm3 then its lateral surface area is ?

  1. 2484 cm2

  2. 2556 cm2

  3. 2520 cm2

  4. 2448 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The triangle with sides 20, 21, 29 is a right triangle (20² + 21² = 29²). Base area = (1/2) × 20 × 21 = 210 cm². Height = Volume / Base area = 7560 / 210 = 36 cm. Lateral surface area = Perimeter × Height = (20 + 21 + 29) × 36 = 2520 cm².

Multiple choice

A sphere with surface area 616 cm2 melted and casted into a circular cone. What will be height of cone if radius of cone is same as that of sphere? (In cm)

  1. 25

  2. 26

  3. 27

  4. 28
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sphere surface area 4πr² = 616, so r² = 49, r = 7 cm. Volume of sphere = (4/3)πr³ = 1437.33 cm³. Cone has same radius (7 cm) and same volume (conserved). (1/3)πr²h = 1437.33, so h = (1437.33 × 3) / (π × 49) = 28 cm. Option C (27 cm) is close but incorrect.

Multiple choice

Find the value of Q1 and Q2 and state the correct relationship.\newline\newlineQuantity I: Area of rectangle whose sides are in the ratio 20 : 9 and perimeter is 116 cm.\newlineQuantity II: Curved surface area of a cylinder of radius 14 cm and height equal to the side of square of area 64 cm$^2$.

  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
A Correct answer
Explanation

Quantity I: Rectangle sides in ratio 20:9, perimeter = 116 cm. Let sides be 20x and 9x. Perimeter = 2(20x + 9x) = 58x = 116, so x = 2. Area = 20x × 9x = 180x² = 180 × 4 = 720 cm². Quantity II: Cylinder radius = 14 cm. Height = side of square with area 64 cm², so side = 8 cm. Curved surface area = 2πrh = 2 × π × 14 × 8 = 224π ≈ 704 cm². Since 720 > 704, Quantity I > Quantity II. However, the claimed answer is A which states 'Quantity I > Quantity II', so agrees = true.

Multiple choice

The side of the triangle are 10cm, 24cm, and 26cm, At each of vertices, circle of the radius 3.5 cm are drawn. What is the area of the triangle excluding the portion covered by the sector of the circle?

  1. 81.5 cm2

  2. 100.75 cm2

  3. 75.75 cm2

  4. 78.25 cm2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Triangle with sides 10, 24, 26 is right-angled (10²+24²=26²). Area = ½ × 10 × 24 = 120 cm². Sectors at vertices have radii 3.5 cm and angles equal to the vertex angles (sum = 180° for right triangle). Total sector area = (180/360) × π × 3.5² = ½ × 38.48 = 19.24 cm². Area excluding sectors = 120 − 19.24 = 100.76 ≈ 100.75 cm². Wait, that assumes sum of angles is 180°, but in a right triangle, the three angles sum to 180°, with one angle = 90°. So total sector area = (90/360 + A/360 + B/360) × πr² = (180/360) × πr² = 19.24. Then 120 − 19.24 = 100.76, which rounds to 100.75. Option B is correct.