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 sides of a triangle are 24 cm, 26 cm and 10 cm. At each of its vertices, circles of radius 4.2 cm are drawn. What is the area (in cm2) of the triangle, excluding the portion covered by the section of the circles?

  1. 120

  2. 27.72

  3. 92.28

  4. 105.86
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sides 24, 26, 10 form a right triangle (10² + 24² = 26²). Area = 1/2 × 10 × 24 = 120 cm². Three circles of radius 4.2 cm at vertices with angles 90°, ~67.38°, ~22.62° cover total sector area = (90+67.38+22.62)/360 × π × 4.2² = 180/360 × (22/7) × 17.64 = 27.72 cm². Triangle excluding circles = 120 - 27.72 = 92.28 cm².

Multiple choice

(\text{The radius of Cylinder is equal to radius circle whose circumference is 88 cm. Find curved surface area of cylinder (in cm²), if height of cylinder is 2 cm.})

  1. 144

  2. 169

  3. 196

  4. 171

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

Circumference=2πr=88, so r=14 cm. Curved surface area of cylinder=2πrh=2π×14×2=56π=175.84 cm² (using π=22/7: 56×22/7=176 cm²). None of the options (144, 169, 196, 171) match 176 or 175.84. Option E is correct.

Multiple choice

Which one of the measurements of the prevailing surface in this region is not correct?

  1. 20 Kachwansi = 1 Biswansi

  2. 20 Biswansi = 10 Biswa

  3. 20 biswa = 1 bigha

  4. 1 bigha = 55 x 55 square yards
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The traditional land measurement system in Uttar Pradesh follows: 20 Kachwansi = 1 Biswansi, 20 Biswansi = 1 Biswa, and 20 Biswa = 1 Bigha. Therefore, option B claiming '20 Biswansi = 10 Biswa' is incorrect - it should be 20 Biswansi = 1 Biswa. 1 Bigha is approximately 55 x 55 square yards in UP. This question asks which measurement is NOT correct, so B is the right answer because it has the wrong conversion.

Multiple choice

The curved surface area of a right circular cone of height 35 cm is , four times of the area of its base, then find the volume of the cone? (Approx)

  1. 2626

  2. 3384

  3. 2994

  4. 3316
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a cone with height h=35 cm, CSA = πrl. Given: πrl = 4×πr² (base area). So l = 4r. Using l² = r² + h²: (4r)² = r² + 35². 16r² = r² + 1225. 15r² = 1225. r² = 81.67, r ≈ 9.04 cm. Volume = (1/3)πr²h = (1/3)×π×81.67×35 ≈ 2994 cm³ (approx).

Multiple choice

The area of the curved surface of a right circular cylinder is 17.5 m2 and its volume is 14 m3. What is the radius of its base?

  1. 0.8

  2. 2

  3. 1.6

  4. 2.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Curved surface area = 2πrh = 17.5, Volume = πr²h = 14. Dividing volume by CSA: (πr²h)/(2πrh) = r/2 = 14/17.5 = 0.8, so r = 1.6. This elegant solution uses the relationship between the two formulas rather than solving for h separately. The radius of 1.6 m is Option C.

Multiple choice

The sum of the radius and height of a cylinder is 25" " cm. The total surface area of the cylinder is 1100cm2. What is the volume of the cylinder?

  1. 2772 cm3

  2. 2744 cm3

  3. 2432 cm3

  4. 2140 cm3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given r + h = 25, so h = 25 - r. Total surface area = 2πr(r + h) = 1100. Substituting: 2πr(25) = 1100, so r = 1100/(50π) = 22/π. Using π = 22/7: r = 22/(22/7) = 14, so h = 25 - 14 = 11. Volume = πr^2h = (22/7) × 14^2 × 11 = (22/7) × 196 × 11 = 22 × 28 × 11 = 2772 cm^3.

Multiple choice

A sphere is melted and molded into a solid cylinder. If the radius of both solids is equal, then find the ratio of the total surface area of the sphere to the total surface area of the cylinder.
  1. $2 : 3$
  2. $4 : 3$
  3. $3 : 7$
  4. $6 : 7$
  5. $7 : 6$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sphere volume = (4/3)πr³ = cylinder volume = πr²h. Height h = 4r/3. Sphere surface area = 4πr². Cylinder surface area = 2πr² + 2πrh = 2πr² + 2πr(4r/3) = 2πr² + 8πr²/3 = 14πr²/3. Ratio = 4πr² : 14πr²/3 = 4 : 14/3 = 12 : 14 = 6 : 7. Option D is correct.

Multiple choice

Ratio between curved surface area and total surface area of a circular cylinder is 3 : 5. If curved surface area is 1848 cm2 then what is the height of cylinder. एक बेलन के वक्र पृष्ठीय क्षेत्रफल और कुल पृष्ठीय क्षेत्रफल का अनुपात 3 : 5 है। यदि वक्र पृष्ठीय क्षेत्रफल 1848 सेमी2 है तो बेलन की ऊँचाई क्या है।

  1. 21

  2. 10.5

  3. 42

  4. 11

  5. 15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a cylinder, CSA : TSA = 2πrh : 2πr(r + h) = 3 : 5. This means 2πrh / [2πr(r + h)] = 3/5, which simplifies to h / (r + h) = 3/5. Cross-multiplying: 5h = 3r + 3h, so 2h = 3r, giving h = 1.5r or r = (2/3)h. Also, CSA = 2πrh = 1848, so 2πr(1.5r) = 1848. With r = 14, we get h = 1.5 × 14 = 21 cm.

Multiple choice

Length of a rectangle is 3 cm more than width of rectangle and the difference between area of circle and area of rectangle is 84 cm2 Find the length of rectangle if radius of circle is 7 cm. एक आयत की लंबाई आयत की चौड़ाई से 3 सेमी अधिक है और वृत्त के क्षेत्रफल और आयत के क्षेत्रफल के बीच का अंतर 84 सेमी2 है यदि वृत्त की त्रिज्या 7 सेमी है तो आयत की लंबाई ज्ञात कीजिए।

  1. 8 cm 8 सेमी

  2. 10 cm 10 सेमी

  3. 7 cm 7 सेमी

  4. 14 cm 14 सेमी

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

Circle area = π(7)² = 154 cm² (taking π = 22/7). Let width = w, then length = w + 3. Rectangle area = w(w + 3). Given: 154 - w(w + 3) = 84, so w(w + 3) = 70. This gives w² + 3w - 70 = 0, or (w + 10)(w - 7) = 0. Since width can't be negative, w = 7 cm. Length = 7 + 3 = 10 cm.

Multiple choice

What is the difference in the volume (in cm3 ) of a sphere of radius 7 cm and that of a cone of radius 7 cm and height 10 cm ? (Use π=22/7)

  1. 205

  2. 704

  3. 924

  4. 1078
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sphere volume = (4/3) × (22/7) × 7³ = (4/3) × (22/7) × 343 = 1,432 2/3 cm³. Cone volume = (1/3) × (22/7) × 7² × 10 = (1/3) × 22 × 7 × 10 = 1,540 1/3 cm³. Wait: let me recalculate. Cone = (1/3) × (22/7) × 49 × 10 = 1,540 cm³ (exactly since 49 cancels with 7). Sphere = (4/3) × 22 × 49 = (4/3) × 1,078 = 1,437 1/3. Difference = 1,540 - 1,437 1/3 = 102 2/3. This doesn't match options. Let me recalculate: (4/3) × (22/7) × 343 = 4,312/3 = 1,437.33. Cone = (1/3) × (22/7) × 49 × 10 = 10,780/21 = 513.33? No, (22/7) × 49 = 154, then × 10 = 1,540, then ÷ 3 = 513.33. So sphere - cone = 1,437.33 - 513.33 = 924.

Multiple choice

The ratio of total surface area of a cylinder to its curved surface area is 18 : 11. If the height of the cylinder is 22 cm, what is the volume (in cm3 ) of the cylinder?

  1. 9034

  2. 10841.6

  3. 13552

  4. 8131.2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a cylinder, total surface area (TSA) = 2πr(r + h) and curved surface area (CSA) = 2πrh. Given TSA:CSA = 18:11, we have 2πr(r + h):2πrh = (r + h):h = 18:11, so r:h = 7:11. With h = 22 cm, r = 14 cm. Volume = πr²h = π(14)²(22) = π(196)(22) = 4312π ≈ 13552 cm³.