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 cone is converted in to the shape of a cylinder of equal radius. If height of the cylinder is 5 cm. The height of the cone is-

  1. 10 cm

  2. 15 cm

  3. 18 cm

  4. 24 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a cone is converted to a cylinder of equal radius, the volume remains the same. Volume of cone = (1/3)πr²h and volume of cylinder = πr²H. Setting them equal: (1/3)πr²h = πr²(5). Cancelling πr² from both sides: (1/3)h = 5, so h = 15 cm. The cone's height must be 3 times the cylinder's height to have equal volumes.

Multiple choice

Sum of volume of cone and volume of cylinder is (15840) cm(^{3}) and height of both cone and cylinder is same i.e. (20) cm. If radius of cylinder is (12) cm then find the ratio of radius of cone to radius of cylinder.

  1. 3: 2

  2. 3: 5

  3. 5: 3

  4. 2: 3

  5. 4: 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cylinder volume = π × 12² × 20 = 1440π cm³. Total volume = 15840 cm³. Cone volume = 15840 - 1440π. Using π ≈ 22/7: 1440π = 1440 × 22/7 = 31680/7 ≈ 4525.7. Cone volume ≈ 15840 - 4525.7 = 11314.3 cm³. Cone volume = (1/3) × π × r² × 20, so r² = (3 × 11314.3)/(20π) ≈ 33942.9/(20 × 22/7) ≈ 33942.9/62.86 ≈ 540. So r ≈ 18 cm. Ratio r_cone : r_cylinder = 18 : 12 = 3 : 2. Option A is correct.

Multiple choice

A solid hemisphere has radius 42 cm. It is melted to form a cylinder such that its curved surface area and the total surface area are in ratio 3: 4. Find the radius of the cylinder.

  1. 12.7 cm

  2. 25.44 cm

  3. 36.10 cm

  4. 49.36 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume conservation: (2/3)π(42)³ = πr²h. Hemisphere volume = 49,392π cm³. For the cylinder, curved surface area = 2πrh and total surface area = 2πr(r+h). Given 2πrh/[2πr(r+h)] = 3/4, we get h/r = 2. Solving with volume gives r = 25.44 cm.

Multiple choice

The cost of gardening of a circular area C at the rate of 10 m2 is Rs 3465. The side of square S is equal to the diameter of circle C. Find the circumference of square S.

  1. 72

  2. 74

  3. 42

  4. 84

  5. 88
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cost of gardening = Rs 3465 at rate of Rs 10 per m² means area = 346.5 m². For circle C: πr² = 346.5, so r² = 346.5/π = 110.25, giving r = 10.5 m. Diameter = 21 m, which is the side of square S. Circumference (perimeter) of square S = 4 × 21 = 84 m.

Multiple choice

The height of a solid cylinder is 8 cm and its base radius is 6 cm, a cone of equal height and the radius is extracted from the cylinder, then find the total surface area of the remaining solid.

  1. 6π cm2

  2. 36π cm2

  3. 192π cm2

  4. 16π cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original cylinder: r = 6 cm, h = 8 cm. After removing cone with same dimensions, the remaining solid has: exposed top ring (outer circle minus cone base) = π(6² - 6²) = 0, curved surface of remaining cylinder portion = 2π(6)(8) = 96π, and base of cylinder = π(6²) = 36π. Also includes inner curved surface (cone lateral area removed) = π(6)(√(6² + 8²)) = 60π. Total = 96π + 36π + 60π = 192π sq.cm. Note: the cone removal creates a cylindrical cavity with curved surface.

Multiple choice

A hollow sphere of outer curved surface area of (324\pi) cm(^{2}) is made from (684\pi) cm(^{3}) of metal. Find the thickness of the hollow sphere.

  1. 2 cm

  2. 3 cm

  3. 4 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let outer radius = R, inner radius = r, thickness = R - r. Outer curved surface = 4πR² = 324π, so R² = 81, R = 9 cm. Volume of metal = (4/3)π(R³ - r³) = 684π. Substituting R = 9: (4/3)(729 - r³) = 684, so 729 - r³ = 513, giving r³ = 216, thus r = 6 cm. Thickness = R - r = 9 - 6 = 3 cm.

Multiple choice

How much area to be painted of the rectangular tank measuring 14 m \times 12 m \times 10 m, if a circular area of radius 1 m is to be left at each surface of the tank?
  1. $871.26 m^{2}$
  2. $883.46 m^{2}$
  3. $893.16 m^{2}$
  4. $837.16 m^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First calculate total surface area of rectangular tank: 2(lb + bh + hl) = 2(14×12 + 12×10 + 10×14) = 2(168 + 120 + 140) = 856 m². Each circular cutout has area πr² = π(1)² ≈ 3.14 m². With 6 surfaces, total cutout area = 6 × 3.14 = 18.84 m². Painted area = 856 - 18.84 ≈ 837.16 m².

Multiple choice

What is the volume of a cone having radius 7 cm. and height 12 cm? 7 सेमी. त्रिज्या और 12 सेमी. ऊंचाई वाले शंकु का आयतन कितना होगा?

  1. 616 cm3

  2. 606 cm3

  3. 614 cm3

  4. 610 cm3

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

Volume of cone = (1/3)πr²h = (1/3) × (22/7) × 7² × 12 = (1/3) × (22/7) × 49 × 12 = (1/3) × 22 × 7 × 12 = (22 × 7 × 12) ÷ 3 = 22 × 7 × 4 = 616 cm³.

Multiple choice

Perimeter of a circle is equal to the perimeter of a square whose area is 1296 cm2 .What is the radius of the circle? एक वृत्त की परिधि 1296 सेमी2 के क्षेत्रफल वाले एक वर्ग की परिधि के समान है। इस वृत्त की त्रिज्या क्या है?

  1. 22.90 cm/सेमी

  2. 11.45 cm/सेमी

  3. 29.20 cm/सेमी

  4. निर्धारित नहीं किया जा सकता

  5. 23.49 cm/सेमी
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Square area=1296, so side=√1296=36. Perimeter=36×4=144. Circle perimeter=2πr=144, so r=144÷(2π)=72÷π≈22.92.