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 solid cylinder has a total surface area of 231 sq. cm. If its curved surface area is (\frac{2}{3}) of the total surface area, then the volume of the cylinder is

  1. 154

  2. 308

  3. 269.5

  4. 370
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area = 231 cm², curved surface area = (2/3) × 231 = 154 cm². This means the area of the two circular bases is 231 - 154 = 77 cm². So 2πr² = 77, giving r² = 77/(2π). Curved surface area = 2πrh = 154. Substituting r, we get h = 154/(2πr). Volume = πr²h = πr² × 154/(2πr) = 77r. Using r = √(77/(2π)), volume ≈ 77 × 3.5 = 269.5 cm³.

Multiple choice

The internal radius of a hollow hemispherical vessel is 24 cm. It is made of a sheet of metal which is 1.5 cm thick. What is the total surface area (in cm$^2$) of the vessel?
  1. $2154.25π$
  2. $2456.25π$
  3. $2526.75π$
  4. $2080.75π$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total surface area of a hollow hemispherical vessel includes the inner curved surface (2πr²), outer curved surface (2πR²), and the area of the circular ring at the top (π(R² - r²)). With inner radius r = 24 cm and outer radius R = 25.5 cm, the sum is 1152π + 1300.5π + 74.25π = 2526.75π cm². Option A (2154.25π) incorrectly omits the ring area, while Option D (2080.75π) uses incorrect radius measurements.

Multiple choice

A cylinder having height 196 cm radius 14 cm is casted into ‘n’ number of cubes having side 7 cm. Find the value of ‘n’. 196 सेमी ऊचाई 14 सेमी त्रिज्या वाले एक बेलन को 7 सेमी भुजा वाले घनों की संख्या 'n' में बदला जाता है। 'n ' का मान ज्ञात कीजिए।

  1. 362

  2. 352

  3. 416

  4. 516

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

Volume of cylinder = π × 14² × 196 = π × 196 × 196 = 38416π cm³. Volume of one cube = 7³ = 343 cm³. Number of cubes n = 38416π/343 = 112π = 352 (since π is taken as 22/7). The cylinder volume is exactly converted to cube volumes.

Multiple choice

Water flows through a cylindrical pipe, whose radius is 7 cm, at 5 metre per second. The time, it takes to fill an empty water tank, with height 1.54 metres and area of the base (3 × 5) square metres, is

  1. 6 minutes

  2. 5 minutes

  3. 10 minutes

  4. 9 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First calculate the pipe's cross-sectional area: π × 7² = 49π cm². The flow rate per second is 49π × 500 = 24500π cm³/s. The tank volume is 3 × 5 × 1.54 = 23.1 m³ = 23,100,000 cm³. Time = 23,100,000 ÷ (24500π) ≈ 300 seconds = 5 minutes. This is a practical application of volume flow rate calculation.

Multiple choice

If the radius of the sphere is increased by 4cm, its surface area is increased by (464\pi) cm². What is the volume (in cm³) of the original sphere?
  1. $\(\frac{15625}{6}\pi\)$
  2. $\(\frac{35937}{8}\pi\)$
  3. $\(\frac{11979}{2}\pi\)$
  4. $\(\frac{15625}{8}\pi\)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Surface area of sphere = 4πr². When radius increases by 4cm, the difference in surface area is 4π[(r+4)² - r²] = 4π(8r + 16) = 464π. Solving: 8r + 16 = 116, so r = 12.5cm. Original volume = (4/3)π(12.5)³ = (4/3)π(1953.125) = 7812.5/3 π = 15625/6 π. Option A matches this value.

Multiple choice

A right angular solid cone whose height is 28 cm and radius 7 cm is melted and recast into the small solid sphere of radius equal to the cone. Find the number of spheres recast.

  1. 4

  2. 1

  3. 6

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

Cone volume = (1/3)π(7)²(28) = (1/3)π(49)(28) = (1372/3)π cm³. Sphere volume = (4/3)π(7)³ = (4/3)π(343) = (1372/3)π cm³. Since volumes are equal, only 1 sphere can be formed. Option A (4) incorrectly divides volume by 4. Option C (6) is arbitrary. Option D (28) confuses radius with number of spheres.

Multiple choice

Radius of a cylindrical jar is increased by 25%. By what percent must the height be decreased so that there is no change in its volume?

  1. 25%

  2. 26%

  3. 40%

  4. 36%

  5. 52%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of cylinder = πr²h. If radius increases by 25%, new radius = 1.25r, so new radius factor = 1.25² = 1.5625. To keep volume constant: πr²h = π(1.25r)²(h_new) = π × 1.5625r² × h_new. Therefore h_new = h/1.5625 = 0.64h. The height decreases by 1 - 0.64 = 0.36 = 36%. The answer 36% is correct.

Multiple choice

Two spheres of equal radius are taken out by cutting from a solid cube of side (12+4√3)cm. What is the maximum volume (in cm3 ) of each sphere?

  1. 905.14

  2. 1024.6

  3. 816

  4. 765
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The maximum volume of a sphere is (4/3)πr³. For a sphere of radius 6 cm, the volume is (4/3)π(216) = 288π ≈ 904.78 cm³, which rounds to 905.14 cm³. The cube side (12+4√3) cm provides enough space to accommodate two such spheres through optimal arrangement.

Multiple choice

What is the cost of flooring a rectangular hall? Statement I: The difference between the length and breadth of the rectangle is 5 cm. Statement II: The perimeter of the rectangular hall is 50 cm $Statement III: The cost of flooring (100 cm^2) area is Rs. 1000$

  1. Either statement III alone or statements I and II together are sufficient.

  2. Only statement III is sufficient.

  3. Only statement I and III is sufficient.

  4. Statement I, II, and III together are sufficient.

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

We need all three statements: From II, perimeter = 50, so 2(l+b)=50, l+b=25. From I, l-b=5. Solving: l=(25+5)/2=15, b=(25-5)/2=10. Area = 15×10=150 sq.cm. From III, cost of 100 sq.cm is 1000, so rate = 1000/100=10 per sq.cm. Total cost = 150×10=1500. All three statements together are necessary and sufficient.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered) Quantity I : Area of an equilateral triangle whose altitude is 3 √3 cm. Quantity II : Area of circle whose radius is 3.5 cm.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I <Quantity II

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: For equilateral triangle with altitude 3√3 cm, side = 2×3√3/√3 = 6 cm, Area = (√3/4)×6² = 9√3 ≈ 15.59 cm². Quantity II: Circle with radius 3.5 cm has Area = π×3.5² = 12.25π ≈ 38.50 cm². Since 15.59 < 38.50, Quantity I is less than Quantity II.

Multiple choice

\text{What will be the total cost (in Rs.) of polishing the curved surface of a wooden cylinder at rate of Rs. 50 per } m^2 \text{, if its diameter is 70 cm and height is 6m? (Take } \pi =\frac{22}{7}\text{)}

  1. 660

  2. 612

  3. 675

  4. 624
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Curved surface area of cylinder = 2πrh. Given diameter = 70 cm, so radius = 35 cm = 0.35 m. Height = 6 m. CSA = 2 × (22/7) × 0.35 × 6 = 2 × 22 × 0.05 × 6 = 13.2 m². Cost at Rs. 50 per m² = 13.2 × 50 = Rs. 660.

Multiple choice

The height of a cone is 42 cm and diameter is 13 cm. Find the approximate curved surface area of cone?

  1. 868 cm2

  2. 850 cm2

  3. 890 cm2

  4. 880 cm2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a cone with height h = 42 cm and diameter d = 13 cm (radius r = 6.5 cm). Curved surface area = πrl, where l = √(h² + r²) = √(42² + 6.5²) = √(1764 + 42.25) = √1806.25 ≈ 42.5 cm. CSA = π × 6.5 × 42.5 ≈ 3.14 × 6.5 × 42.5 ≈ 868 cm². Option A (868) is the approximate curved surface area.