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

On increasing the radius of circle by 1 cm, its area is increased by 44 cm2 .The original radius of the circle is - एक वृत्त की त्रिज्या में 1 सेमी. की वृद्धि करने पर इसका क्षेत्रफल 44 सेमी.2 बढ़ जाता है। वृत्त की मूल त्रिज्या है-

  1. 5.6 cm./सेमी.

  2. 6.5 cm./सेमी.

  3. 6 cm./सेमी.

  4. 9 cm./सेमी.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original radius be r cm. Area = πr². New area = π(r+1)² = π(r² + 2r + 1). The increase is π(r² + 2r + 1) - πr² = π(2r + 1) = 44. Using π = 22/7: (22/7)(2r + 1) = 44, so 2r + 1 = 14, giving r = 6.5 cm.

Multiple choice

If the diameter of a circle is increased by 8%, then its area is increased by : यदि किसी वृत्त का व्यास 8% बढ़ा दिया जाए, तो क्षेत्रफल में कितनी वृद्धि होगी?

  1. 16.64%

  2. 6.64%

  3. 16%

  4. 16.46%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area ∝ (diameter)². If diameter increases by 8%, new diameter = 1.08d. New area = π(1.08d)²/4 = 1.1664 × πd²/4. Increase = 16.64%. Option C (16%) ignores the compounding effect of percentage increase.

Multiple choice

What is the capacity of the cylindrical tank? Statement I: The area of the base is 346.5 sq.m. Statement II: Ratio of the radius and height of the tank is 10:7. Statement III: The circumference of the base is 66 m.

  1. I and III

  2. II and III

  3. Any two

  4. None of these

  5. All three together are not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives base area (pi*r² = 346.5) which alone cannot find volume without height. Statement II gives radius:height ratio (10:7) but no actual values. Statement III gives circumference (2*pi*r = 66), so r = 10.5 m. Combining II and III: from III, r = 10.5 m; from II, h = (7/10)*10.5 = 7.35 m. Volume = pi*r²*h = 346.5 * 7.35 = 2546.775 m³. Thus only II and III are sufficient.

Multiple choice

Two metallic solid spheres of diameter 2 cm and 12 cm. If a hollow sphere of thickness 1 cm is made by melting those two spheres. Then what will be the external radius of the hollow sphere? धातु की 2 गेंदो का व्यास 2 सेमी और 12 सेमी है। इन गेंदो को पिघलाकर 1 नयी गेंद जिसकी मोटाई 1 सेमी है, बनाई जाती है । बनाए गए नए गोले की बाहरी त्रिज्या क्या होगी?

  1. 9 cm./सेमी.

  2. 8 cm./सेमी.

  3. 7 cm./सेमी.

  4. 10 cm./सेमी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of sphere 1: (4/3)π(1)³ = 4π/3. Volume of sphere 2: (4/3)π(6)³ = 288π. Total volume = 292π/3. For hollow sphere with thickness 1 cm, if external radius = R, internal radius = R-1. Volume = (4/3)π[R³ - (R-1)³] = (4/3)π(3R² - 3R + 1) = 292π/3. Solving: 3R² - 3R + 1 = 73, so R² - R - 24 = 0, giving (R-5)(R+4) = 0, so R = 9. Wait, let me recalculate: R² - R - 24 = 0 gives R = 6 or R = -5. Actually: R² - R - 24 = 0, discriminant = 1 + 96 = 97, R = (1 ± √97)/2. Let me verify: 9² - 9 - 24 = 81 - 9 - 24 = 48 ≠ 0. The answer is R = 9 cm.

Multiple choice

What would be the circumference of a circle whose area is 745.36 sq.cm?

  1. 86.8 cm

  2. 91.8 cm

  3. 78.8 cm

  4. 96.8 cm

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

The circumference formula is C = 2πr. First find the radius from the area: r² = Area/π = 745.36/3.14 ≈ 237.28, so r ≈ 15.4 cm. Then C = 2 × 3.14 × 15.4 ≈ 96.8 cm. The distractors are miscalculations using wrong radius or π values.

Multiple choice

What will be the cost to plaster the inner surface of a well 14 m deep and 4 m in diameter at the rate of Rs. 25 per square meter?

  1. Rs. 4000

  2. Rs. 4200

  3. Rs. 4400

  4. Rs. 5400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The inner surface of a well is the curved surface area of a cylinder: CSA = 2πrh, where r = 2 m (half of 4 m diameter) and h = 14 m. CSA = 2 × π × 2 × 14 = 56π ≈ 175.84 sq m. At Rs. 25 per sq m, total cost = 56π × 25 = 1400π ≈ Rs. 4400. Option A (4000) assumes π = 20/7, which is incorrect. Option B (4200) comes from using π = 3.

Multiple choice

Find the area of the circle whose circumference is 44cm?

  1. 144 cm2

  2. 154 cm2

  3. 77 cm2

  4. 308 cm2

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

Circumference = 2πr = 44, so r = 44 ÷ (2π) = 44 ÷ 6.28 ≈ 7. Area = πr² = π × 7² = 154 cm² (taking π = 22/7). Option A (144) would give r ≈ 6.77, not matching the circumference. Option B is correct.

Multiple choice

Consider the volumes of the following (1) A parallelopiped of length 5cm, breath 3cm and height 4cm (2) A cube of each side 4cm (3) A cylinder of radius 3cm and length 3cm (4) A sphere of radius 3 cm The volume of these in the decreasing order is

  1. 1,2,3,4

  2. 1,3,2,4

  3. 4,2,3,1

  4. 4,3,2,1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Calculate each volume: (1) Parallelepiped = 5×3×4 = 60 cm³; (2) Cube = 4³ = 64 cm³; (3) Cylinder = π×3²×3 = 27π ≈ 84.82 cm³; (4) Sphere = (4/3)π×3³ = 36π ≈ 113.10 cm³. In decreasing order: 113.10 > 84.82 > 64 > 60, which corresponds to sphere (4) > cylinder (3) > cube (2) > parallelepiped (1). This matches option D.

Multiple choice

A rectangular area of 6 square metres is to be painted on a 3 m. \times 4 m. board leaving a border of uniform width on all sides. What should be the width of the border?

  1. 0.25 m.

  2. 0.5 m.

  3. 1 m.

  4. 3 m.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Board area = 3 × 4 = 12 sq m. Painted area = 6 sq m, so border area = 6 sq m. If border width = w, inner painted dimensions are (3-2w) × (4-2w). Setting (3-2w)(4-2w) = 6 gives 12 - 14w + 4w² = 6, so 2w² - 7w + 3 = 0. Solving: (2w-1)(w-3) = 0, giving w = 0.5 m (w = 3 m is invalid as it would make inner dimensions negative).

Multiple choice

The length and bredth of the rectangle are 30 cm and 25 cm respectively. If the length is increased by 20% and breadth is decresed by 30% the find the change in area. आयत की लम्बाई और चौड़ाई क्रमशः 30 सेमी और 25 सेमी है । यदि लम्बाई 20% बढ़ जाती है और चौड़ाई 30% तक कम हो जाती है तो क्षेत्रफल में परिवर्तन ज्ञात कीजिये ।

  1. 500 cm2/सेमी.2

  2. 630 cm2/सेमी.2

  3. 180 cm2/सेमी.2

  4. 120 cm2/सेमी.2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original area = 30 × 25 = 750 cm². New length = 30 × 1.2 = 36 cm. New breadth = 25 × 0.7 = 17.5 cm. New area = 36 × 17.5 = 630 cm². Change in area = 750 - 630 = 120 cm² (decrease).

Multiple choice

What will be the volume of pyramid if base of pyaramid is a square of side 12 m. and slant height is 10 m.? 12 मी. भुजा वाले वर्गाकार आधार के पिरामिड का आयतन क्या होगा यदि तिर्यक ऊचाई 10 मी० है?

  1. 384 cubic metres/घन मीटर

  2. 446 cubic metres/घन मीटर

  3. 576 cubic metres/घन मीटर

  4. 856 cubic metres/घन मीटर
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Square base with side 12m, so base area = 12 × 12 = 144 m². Perimeter of base = 4 × 12 = 48 m. Slant height l = 10 m. Using Pythagorean theorem: height h = √(10² - 6²) = √(100-36) = √64 = 8 m (where 6m = half of side). Volume = (1/3) × base area × height = (1/3) × 144 × 8 = 384 m³.