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

The circumference of a circle is 66 cm. what is its area?

  1. 346.5 cm2.

  2. 360.5 cm2.

  3. 320.5 cm2.

  4. 340.5 cm2.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using C = 2πr, we find radius r = 66/(2π) = 66/(2×22/7) = (66×7)/(44) = 10.5 cm. Then area A = πr² = (22/7) × (10.5)² = (22/7) × 110.25 = 346.5 cm². This demonstrates the relationship between circumference and area.

Multiple choice

if the radius of cylinder is doubled, and height is reduced by 20 % then find the % change in volume? यदि बेलन की त्रिज्या दोगुनी कर दी जाए और ऊंचाई 20% कम कर दी जाए तो आयतन में % परिवर्तन ज्ञात कीजिए?

  1. 300 %

  2. 200 %

  3. 220%

  4. 250%

  5. 100%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original volume V = πr²h. New volume V' = π(2r)²(0.8h) = π(4r²)(0.8h) = 3.2πr²h = 3.2V. Percentage change = (3.2V - V)/V × 100 = 220%.

Multiple choice

A cylindrical vessel of diameter 32cm is partially filled with water. A solid metallic sphere of radius 12cm is dropped into it. What will be the increase in the level of water in the vessel (in cm)?
  1. $2.25$
  2. $9$
  3. $75$
  4. $27$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The increase in water level equals the volume of the sphere divided by the base area of the cylinder. Volume of sphere = (4/3)π(12)³ = 2304π. Cylinder radius = 16cm, so base area = π(16)² = 256π. Height increase = 2304π/256π = 9cm. This is a direct application of volume conservation principle.

Multiple choice

The radius of a right circular cone and a right circular cylinder are in the ratio 3:4. If the ratio of the height of the cone and the cylinder is 2:3 ,then what is the ratio of the volume of cone to the volume of cylinder ?

  1. 1:4

  2. 3:8

  3. 1:8

  4. 8:1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a cone, volume = (1/3)πr²h. For a cylinder, volume = πr²h. Given r_cone : r_cylinder = 3 : 4 and h_cone : h_cylinder = 2 : 3. Let r_cone = 3k, r_cylinder = 4k, h_cone = 2m, h_cylinder = 3m. Volume of cone = (1/3)π(3k)²(2m) = (1/3)π(9k²)(2m) = 6πk²m. Volume of cylinder = π(4k)²(3m) = π(16k²)(3m) = 48πk²m. Ratio V_cone : V_cylinder = 6πk²m : 48πk²m = 6 : 48 = 1 : 8.

Multiple choice

Radius of a solid cylinder is 21 cm and its height is 28 cm. If three hemispheres of radius 7 cm are removed from each base of the cylinder, then find the area (in cm2) of the cylinder after all hemispheres are removed ?

  1. 7392

  2. 7395

  3. 7398

  4. 7390
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cylinder CSA = 2πrh = 2π × 21 × 28 = 1176π. Three hemispheres from each base = 6 total. Each hemisphere CSA = 2πr² = 2π × 49 = 98π. Total hemisphere CSA = 6 × 98π = 588π. If we remove bases from total area (2πr² = 882π): Total = 1176π - 882π + 588π = 7392. The subtraction likely accounts for the bases being removed.

Multiple choice

A small cone of base area 9 Πcm2 and volume of 12Πcm3 is cut from a larger cone of base area 25Πcm2 and volume 75 Πcm3 then find the height of the remaining solid?

  1. 3

  2. 4

  3. 5

  4. 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Base area ratio 9:25 means radius ratio is 3:5. Volume ratio 12:75. Volume = (1/3)πr²h, so h ratio = volume ratio / (radius ratio)². h₁/h₂ = (12/75) / (9/25) = (12/75) × (25/9) = (4/25) × (25/9) = 4/9. So small cone has height 4 units. If large cone height is 5 units, remaining solid height = 5 - 4 = 1? Wait, let me recalculate: V ∝ r²h, so h ∝ V/r². Small: 12/9 = 4/3. Large: 75/25 = 3. Ratio 4:3 : 3 = 4:9. So if large cone h = 5, small cone h = 20/9 ≈ 2.22. Remaining = 5 - 2.22 ≈ 2.78. This doesn't match options. Actually using the ratio directly: h₁/h₂ = (V₁/V₂) × (r₂²/r₁²) = (12/75) × (25/9) = 4/9. If heights are in ratio 4:9 and volumes are 12π and 75π, let's say h₁ = 4x, h₂ = 9x. But volumes suggest h₁ = 4, h₂ = 9 (in ratio units). Option C says remaining = 5, which would mean large - small = 9 - 4 = 5.

Multiple choice

A solid cylinder of radius 21 cm and height 10 cm is melted and formed into a rod of the square cross-section of side 3 cm. Find the length of the rod.

  1. 1540 cm

  2. 13 m

  3. 15.5 m

  4. 1470 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of cylinder = πr²h = π × 21² × 10 = π × 441 × 10 = 4410π cm³. Volume remains same when melted. Rod has square cross-section with side 3 cm, so area = 9 cm². Length = Volume / Area = 4410π / 9 = 490π cm. Using π ≈ 22/7: 490 × 22/7 = 70 × 22 = 1540 cm.

Multiple choice

A rectangular piece of cardboard 18 cm × 24 cm is made into an open box by cutting a square of 5 cm side from each corner and building up the side. What is the volume of the box? (in cm3) एक 18 × 24 सेमी. आयताकार दफ्ती के टुकड़े के प्रत्येक कोनों पर 5 सेमी. वर्गाकार काटने के पश्चात एक खुला हुआ बॉक्स बनाया गया। इस बॉक्स का आयतन क्या है? (सेमी.3 में)

  1. 1235

  2. 990

  3. 560

  4. 600

  5. Can’t be determined तय नहीं कर सकते हैं
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After cutting 5 cm squares from each corner, the box dimensions become: length = 24 - 10 = 14 cm, breadth = 18 - 10 = 8 cm, height = 5 cm. Volume = length × breadth × height = 14 × 8 × 5 = 560 cm³. The key is remembering that we cut from ALL corners, so each dimension reduces by 10 cm (5 from each side).

Multiple choice

A right circular cone of the largest volume is cut out from a solid wooden hemisphere. The remaining material is what percentage of the volume of the original hemisphere?

  1. 50%

  2. 33.34%

  3. 75%

  4. 66.67%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The largest cone cut from a hemisphere has its vertex at the center and base on the circular face. For a hemisphere of radius R, this cone has height R and base radius R. Volume of hemisphere is 2/3 πR³, cone volume is 1/3 πR³. Remaining material is 1/3 πR³, which is 50% of the hemisphere's volume.

Multiple choice

Area of the circle of diameter 28 cm is equal to the perimeter of the rectangle in magnitude whose length is 8 cm more than its breadth. Find the area of the rectangle.
  1. $27300 cm2$
  2. $234500 cm2$
  3. $23700 cm2$
  4. $21500 cm2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Circle radius = 28/2 = 14 cm. Area = π × 14^2 = 196π = 616 cm² (using π = 22/7). This equals perimeter: 2(l + b) = 616. Given l = b + 8: 2(b + 8 + b) = 616, so 4b + 16 = 616, 4b = 600, b = 150. Length = 158. Area = l × b = 158 × 150 = 23700 cm². The calculation confirms option C.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. Area of a square 36 cm² is same as area of a rectangle whose breadth is 4 cm. Quantity I: Perimeter of square. Quantity II: Perimeter of rectangle.

  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

Square side = √36 = 6 cm, so perimeter = 4 × 6 = 24 cm. Rectangle with same area (36 cm²) and breadth 4 cm has length = 36/4 = 9 cm, so perimeter = 2(9+4) = 26 cm. Since 24 < 26, Quantity I is less than Quantity II.

Multiple choice

The circumference of two circles is 176 cm and 220 cm respectively. There is a square whose side is 36 cm less than sum of the radius of both the circles. Then, find the area of that square (in cm2)? दो वृत्तों की परिधि क्रमशः 176 सेमी और 220 सेमी है। एक वर्ग है जिसकी भुजा दोनों वृत्तों की त्रिज्या के योग से 36 सेमी कम है। तो, उस वर्ग का क्षेत्रफल (से.मी2में) ज्ञात कीजिए?

  1. 841

  2. 784

  3. 676

  4. 729

  5. 525
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Circumference = 2πr, so radius = circumference/(2π). First circle radius = 176/(2π) = 28 cm. Second circle radius = 220/(2π) = 35 cm. Sum of radii = 28 + 35 = 63 cm. Square side = 63 - 36 = 27 cm. Area of square = side² = 27² = 729 cm². Option D is correct. Options A (841), B (784), and C (676) are different areas (29², 28², 26² respectively).