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

If the ratio of curved surface area of cylinder to the volume of cylinder is 2: 21 while the ratio of diameter of cylinder to the height of cylinder is 7:3. Find the total surface area of cylinder?

  1. 5148 m2

  2. 5146 m2

  3. 5040 m2

  4. 4851 m2

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

Let radius = r and height = h. Curved surface area = 2πrh, volume = πr²h. Given CSA:Volume = 2:21, so 2πrh / πr²h = 2/21, which gives 2/r = 2/21, so r = 21. Also given diameter:height = 7:3, so 2r/h = 7/3. With r = 21, we get h = 18. Total surface area = 2πr(r+h) = 2π × 21 × 39 = 1638π ≈ 5148 m² (using π ≈ 22/7). Option A is correct.

Multiple choice

The sum of circumference of a circle and perimeter of a square is 210 cm. The diameter of the circle is 21 cm. What is the sum of area of circle and square? एक वृत्त की परिधि और एक वर्ग के परिमाप का योग 210 सेमी है। वृत्त का व्यास 21 सेमी है। वृत्त और वर्ग के क्षेत्रफल का योग क्या है?

  1. 1722.50 cm2 1722.50 सेमी2

  2. 1590.75 cm2 1590.75 सेमी2

  3. 1482.25 cm2 1482.25 सेमी2

  4. 1642.50 cm2 1642.50 सेमी2

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

Given: Circumference + Perimeter = 210 cm, Diameter = 21 cm. Circumference = π × diameter = π × 21 = 66 cm (approx). So Perimeter of square = 210 - 66 = 144 cm. Side of square = 144/4 = 36 cm. Area of circle = π × r² = π × (10.5)² = 346.36 cm². Area of square = side² = 36² = 1296 cm². Total = 346.36 + 1296 = 1642.36 cm² ≈ 1642.50 cm². The answer matches option D.

Multiple choice

If a right circular solid cylinder of base radius 7 cm and height 28 cm is melted to form a cuboid such that the ratio of its side is 2 : 3 : 6. Then find the total surface area (in sq. cm) of cuboid?

  1. 72×(1078/9)(2/3)

  2. 36×(2156/9) (2/3)

  3. 72×(2156/9) (2/3)

  4. 36×(1078)(2/3)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cylinder volume = πr²h = π × 7² × 28 = 4312π/3 cm³ (using π = 22/7). This becomes cuboid volume. If sides are in ratio 2:3:6, let sides be 2k, 3k, 6k. Volume = 36k³ = 4312π/3, so k³ = 1078π/9 and k = (1078π/9)^(1/3). Surface area = 2(2k×3k + 2k×6k + 3k×6k) = 2(6k² + 12k² + 18k²) = 72k² = 72 × (1078π/9)^(2/3). This matches option A. The other options have incorrect coefficients or fractional powers.

Multiple choice

Pawan has a solid sphere of radius 21 cm. He melted it to form a cube. 20% material is wasted in this process. He melted the cube to form hemisphere. In this process 20% material is wasted. He again melted hemisphere to form two spheres of equal radius. 20% material was again wasted in this process. Then find the radius (in cm) of each new sphere?

  1. 4.2(∛2)

  2. 2.2(∛2)

  3. 2.2(∛4)

  4. 8.4(∛4)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original sphere volume = (4/3)π × 21³ = 4116π cm³. After 20% waste in forming cube: remaining = 0.8 × 4116π. Cube volume = (0.8 × 4116π) = side³. After 20% waste to hemisphere: remaining = 0.64 × 4116π. Hemisphere volume = (0.64 × 4116π) = (2/3)πr³. After 20% waste to 2 new spheres: total remaining = 0.512 × 4116π = 2 × (4/3)πR³. Solving: R³ = (0.512 × 4116π × 3)/(8π) = 793.824. R = ∛793.824 = 8.4∛4 cm. Options A, B, and C have incorrect coefficients or cube roots.

Multiple choice

In a right circular cone the radius of its base is 6 cm and its height is 14 cm. A cross section is made through the mid-point of the height parallel to the base. The volume of the lower position is? एक गोलाकार शंकु में इसके आधार की त्रिज्या 6 सेमी है और इसकी ऊँचाई 14 सेमी है। एक क्रॉस सेक्शन को आधार के समानांतर ऊंचाई के मध्य-बिंदु के माध्यम से बनाया गया है। निम्न स्थिति का आयतन है?

  1. 528

  2. 366

  3. 498

  4. 462

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

The full cone volume is (1/3)πr²h = (1/3)π(6)²(14) = 168π cm³. When cut at the midpoint of height (7cm), the radius at that level is 3cm by similarity. The upper small cone has volume (1/3)π(3)²(7) = 21π cm³. Therefore, the lower frustum volume = 168π - 21π = 147π ≈ 462 cm³. The key is recognizing the smaller cone removed from the top.

Multiple choice

If Sum of volume of cone (A) and volume of cylinder (H) is 5040 π cm^3 and height of both cone and cylinder is same that is 20 cm and radius of cylinder is 12 cm, then what is the ratio of radius of A to radius of H.

  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

Volume of cone = (1/3)πr_A²h and volume of cylinder = πr_H²h. Given total volume = 5040π, h = 20, and r_H = 12, we substitute: (1/3)πr_A²(20) + π(12)²(20) = 5040π. Simplifying gives (20/3)πr_A² + 1440π = 5040π, so (20/3)πr_A² = 3600π, giving r_A² = 540. Thus r_A = √540 = 6√15, and the ratio r_A : r_H = 6√15 : 12 = √15 : 2 = 3:2.

Multiple choice

The ratio of volume of a cone to that of a cylinder if radius of cylinder is 1/4 times of that of cone and its height is 8 times of that of the cone, is - एक शंकु के आयतन का एक बेलन के आयतन से अनुपात है, यदि बेलन की त्रिज्या शंकु की त्रिज्या की 1/4 गुना है और इसकी ऊंचाई शंकु की 8 गुना है

  1. 3:2

  2. 2:3

  3. 4:5

  4. 5:4

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

Volume of cone = (1/3)πr²h and volume of cylinder = πR²H. Given R = (1/4)r and H = 8h, substituting gives cylinder volume = (1/2)πr²h. The ratio cone:cylinder = (1/3):(1/2) = 2:3. The answer is not 3:2 (option A) which reverses the ratio.

Multiple choice

If the cost of gardening a circular field at the rate of 10 Rs./ m2 is Rs. 3465 and the side of a square is equal to the diameter of the circle. Then find the perimeter of the square ?

  1. 76

  2. 92

  3. 84

  4. 68

  5. 65
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Circle area = cost/rate = 3465/10 = 346.5 m². Area = πr², so r = √(346.5/π) ≈ 10.5m. Diameter = 2r ≈ 21m. Square side = diameter = 21m. Perimeter = 4 × side = 4 × 21 = 84m. The key relationship is that the square's side equals the circle's diameter.

Multiple choice

Find the area of the circle whose radius is equal to the radius of a cylinder having height 21 cm and volume 12936 cm3 ? उस वृत्त का क्षेत्रफल ज्ञात कीजिए जिसका त्रिज्या एक बेलन की त्रिज्या के बराबर है जिसकी ऊँचाई 21 सेमी और आयतन 12936 सेमी2है?

  1. 544 cm2

  2. 196 cm2

  3. 154 cm2

  4. 616 cm2

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

Volume of cylinder = πr²h. Given h=21 cm and V=12936 cm³, we get r² = 12936/(21π) = 616/π. Area of circle = πr² = π × (616/π) = 616 cm². The key insight is that π cancels out - you only need r², not r itself.

Multiple choice

What is the cost of flooring a rectangular hall? (\)\n(A) The length and the breadth of the hall are in the ratio of 3:2. (\)\n(B) The length of the hall is 48 m and the cost of flooring is Rs 850 per square metre. (\)\n(C) The perimeter of the hall is 160 m and the cost of flooring is Rs 850 per square metre.

  1. Only A and B

  2. Only A and C

  3. Only C

  4. Any two of the three

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

Statement B alone is sufficient as it gives length and cost per square meter, allowing area and cost calculation. However, combined with A (ratio) or C (perimeter), we can find breadth. 'Any two statements' works as A+B or B+C both yield the dimensions needed.

Multiple choice

(\text{If whole surface area of a sphere is } 100\pi \text{, then radius will be})

  1. 4

  2. 7

  3. 4.5

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

Surface area of a sphere = 4πr². Given 4πr² = 100π. Dividing both sides by 4π: r² = 25. Taking square root: r = 5. So the radius is 5 units. Remember to divide the total surface area by 4π first before taking the square root. Options like 4, 4.5, and 7 would give surface areas of 64π, 81π, and 196π respectively, none of which equal 100π.

Multiple choice

What is the area of a circle whose circumference is 264 cm?
  1. $5544 sq. cm$
  2. $5454 sq. cm$
  3. $5540 sq. cm$
  4. $5548 sq. cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Circumference C = 2πr = 264 cm. Therefore radius r = 264/(2π) = 264/44 = 6 cm (using π = 22/7). Area A = πr² = (22/7) × 6² = (22/7) × 36 = 22 × 36/7 = 792/7 = 113.14... Wait, let me recalculate: (22/7) × 36 = 792/7 ≈ 113.14. But using π = 22/7: r = 264/(2 × 22/7) = 264 × 7/44 = 6. Area = (22/7) × 36 = 792/7 = 113.14. Hmm, this doesn't match 5544. Let me use r = 264/2π. If π=22/7, r=264/(44/7)=264×7/44=42. Then area = (22/7) × 42² = (22/7) × 1764 = 22 × 252 = 5544 sq. cm.

Multiple choice

If the radius of circle is increased by 4 times, what will be the percentage increase in its area? यदि एक वृत्त की त्रिज्या में 4 गुना वृद्धि कर दी जाए, तो इसके क्षेत्रफल में प्रतिशत वृद्धि कितनी होगी?

  1. 300%

  2. 400%

  3. 1500%

  4. 1600%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When radius increases by 4 times, the new area becomes (4r)^2 = 16r^2, which is 16 times the original area. This represents a 1500% increase since (new area - original area) / original area × 100 = (16-1)/1 × 100 = 1500%. Option C (1500%) is correct.