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 radius of two circles are 19 cm. and 9 cm. respectively. Find the area of the circle which has its circumference equal to the sum of the circumferences of the two circles. दो वृत्तों की त्रिज्यायें क्रमशः 19 सेमी. और 9 सेमी. हैं। उस वृत्त का क्षेत्रफल ज्ञात कीजिए जिसका परिमाप दोनों वृत्तों के परिमाप के योग के बराबर है।

  1. 2464 cm2 /सेमी2

  2. 2644 cm2 /सेमी2

  3. 2446 cm2 /सेमी2

  4. 4246 cm2 /सेमी2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Circumference of first circle = 2π × 19 = 38π. Circumference of second = 2π × 9 = 18π. Sum = 56π. For new circle: 2πR = 56π, so R = 28 cm. Area = π(28)² = 784π = 784 × 22/7 = 2464 cm². The radius of the new circle is the sum of individual radii when adding circumferences.

Multiple choice

A ball of radius 1 m is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m. What is the curved surface area of the pipe ? किसी बेलनाकार पाइप में 1 मी. त्रिज्या वाली एक गेंद डाली गई है जो इसमें पूरी तरह फिट हो जाती है। यदि पाइप की लम्बाई 14 मी. है। तो पाइप का पार्श्वपृष्ठीय क्षेत्रफल ज्ञात कीजिए।

  1. 176 m2/मी2

  2. 84 m2/मी2

  3. 88 m2/मी2

  4. 96 m2/मी2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since the ball of radius 1 m fits exactly inside the pipe, the pipe's internal radius must be 1 m (the ball's diameter equals the pipe's diameter). The curved surface area of a cylinder is 2πrh. Substituting r = 1 m and h = 14 m gives 2π × 1 × 14 = 28π ≈ 88 m² (using π = 22/7).

Multiple choice

Radius of a sphere is increased by 15%. Find the percentage change in its volume (Approx) एक गोले की त्रिज्या 15 प्रतिशत बढ़ा दी गयी। इसके आयतन में प्रतिशत वृद्धि ज्ञात करें (लगभग)-

  1. 24%

  2. 41%

  3. 15%

  4. 52%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of a sphere is proportional to the cube of its radius (V = 4/3πr³). When radius increases by 15%, the new radius is 1.15r. The new volume becomes (1.15)³ = 1.520875 times the original, representing a 52.0875% increase, which rounds to approximately 52%. This uses the compound percentage change formula: (1 + 15/100)³ - 1 = 0.520875 or 52.0875%.

Multiple choice

Volume of sphere is increased by 119.7%. Find the percentage change in its radius. एक गोले का आयतन 119.7% बढ़ गया। इसकी त्रिज्या में प्रतिशत वृद्धि ज्ञात कीजिए।

  1. 25%

  2. 15%

  3. 10%

  4. 30%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume increases by 119.7%, so new volume = 2.197 × original. Volume formula V = 4/3πr³. New radius: r' = r × (2.197)^(1/3) = r × 1.3. Percentage increase = (1.3 - 1) × 100 = 30%. Cube root of 2.197 ≈ 1.3.

Multiple choice

A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase (in cm.2) in the total surface area? 7 से.मी. व्यास वाले एक ठोस गोले को दो बराबर भागों में काटा जाता है। कुल पृष्ठीय क्षेत्रफल में कितनी वृद्धि (से.मी.2 में) होगी?

  1. 77

  2. 154

  3. 87

  4. 38.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original sphere: radius = 3.5 cm, total surface area = 4πr² = 4 × (22/7) × (3.5)² = 154 cm². When cut into two hemispheres, each hemisphere has curved surface area 2πr² and one flat circular face πr². Total for two hemispheres = 2(2πr² + πr²) = 6πr² = 308 cm². Increase = 308 - 154 = 154 cm². Option B is correct.

Multiple choice

Find the area of the ring between two concentric circles, whose circumference are 88 cm. and 132 cm. दो संकेद्रीय वृत्तों के घेरे के बीच का क्षेत्रफल ज्ञात कीजिये जिनकी परिधि 88 सेमी. और 132 सेमी. है।

  1. 780 cm.2/सेमी.2

  2. 770 cm.2/सेमी.2

  3. 715 cm.2/सेमी.2

  4. 660 cm.2/सेमी.2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From circumference 2πr = 88 and 132, we get r = 14 cm and 21 cm. The ring's area is π(21² - 14²) = π(441 - 196) = 245π ≈ 770 cm².

Multiple choice

The height of a cone is 21 cm. and radius of its base is 28 cm. Find its total surface area. एक शंकु की ऊँचाई 21 सेमी. है और इसके आधार की त्रिज्या 28 सेमी. है। इसका सम्पूर्ण पृष्ठ का क्षेत्रफल ज्ञात कीजिए।

  1. 4444 cm.2/सेमी.2

  2. 4642 cm.2/सेमी.2

  3. 5544 cm.2/सेमी.2

  4. 6655 cm.2/सेमी.2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area of cone = πr(r + l), where l = √(h² + r²). Here l = √(21² + 28²) = √(441 + 784) = √1225 = 35 cm. Surface area = (22/7) × 28 × (28 + 35) = 88 × 63 = 5544 cm².

Multiple choice

The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross section. If the length of the wire is 36 m., then what is its radius equal to? एक धात्वीय गोले का व्यास 6 सेमी. है। गोले कीो पिघलाया जाता है और एक समान वृत्तीय अनुप्रस्थ काट वाले तार में परिविर्तत किया जाता है। यदि तार की लम्बाई 36 मी. है, तो त्रिज्या किसके बराबर है-

  1. 0.1 cm/सेमी.

  2. 0.01 cm/सेमी.

  3. 0.001 cm/सेमी.

  4. 1.0 cm/सेमी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sphere volume = (4/3)π(3)³ = 36π cm³. This equals the wire volume: πr²(3600). Solving: r² = 36/(3600) = 1/100, so r = 0.1 cm. Note the unit conversion: wire length is 36 m = 3600 cm. Volume remains constant during melting and reshaping.

Multiple choice

The area of circle is 24.64 m2. The circumference of the circle is - एक वृत्त का क्षेत्रफल 24.64 मी2 है, उस वृत्त की परिधि क्या होगी?

  1. 14.64 m./मी.

  2. 16.36 m./मी.

  3. 17.60 m./मी.

  4. 18.40 m./मी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area = πr² = 24.64. Taking π = 22/7, r² = 24.64 × 7/22 = 7.84, so r = 2.8 m. Circumference = 2πr = 2 × 22/7 × 2.8 = 17.6 m.

Multiple choice

The curved surface of a cylinder is 4400 cm.2 and its circumference of the base is 110 cm. find the volume of cylinder.

  1. 36700 cm.3

  2. 36720 cm.3

  3. 38500 cm.3

  4. 39600 cm.3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Curved surface area = 2πrh = 4400. Circumference = 2πr = 110, so r = 110/2π = 55/π. Substituting: 2π(55/π)h = 4400, giving 110h = 4400, so h = 40. Volume = πr²h = π(55/π)² × 40 = π(3025/π²) × 40 = (3025 × 40)/π = 121000/π ≈ 38500 (taking π = 22/7). Option C (38500) is correct.

Multiple choice

Find the circumference of the circle whose area is 452.57 cm2.(Approx)

  1. 67.5 cm

  2. 70 cm

  3. 85 cm

  4. 75.5 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Area of circle = πr² = 452.57 cm². So r² = 452.57/π ≈ 144, giving r ≈ 12 cm. Circumference = 2πr ≈ 2 × 3.14 × 12 = 75.36 cm. The closest option is 75.5 cm. Using π ≈ 3.14: r = √(452.57/3.14) ≈ 12.001 cm, C ≈ 75.4 cm.

Multiple choice

The sum of areas of a circle and a rectangle is 1166 sq. cm.The diameter of circle is 28 cm. If the length of rectangle is 25 cm then what is the sum of circumference of circle and perimeter of rectangle.

  1. 186 cm

  2. 182 cm

  3. 184 cm

  4. Can't be determined

  5. 174 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Circle radius = 28/2 = 14 cm. Circle area = π(14)² ≈ 616 cm². Rectangle area = 1166 - 616 = 550 cm². Rectangle width = 550/25 = 22 cm. Rectangle perimeter = 2(25+22) = 94 cm. Circle circumference = 2π(14) ≈ 88 cm. Total = 94 + 88 = 182 cm. The key is finding the rectangle width from area difference.

Multiple choice

What is the largest number of pipes of the shape of right circular cylinders with length 10 cm. and radius 1 cm. that can be fitted into a box, all of whose sides are 20 cm. in length? 10 सेमी. लम्बी और 1 सेमी. त्रिज्या की सम वृत्तीय बेलनाकार की कितनी पाइपों को एक बॉक्स में रखा जा सकता है, जिसकी सभी भुजाओं की लम्बाई 20 सेमी. है?

  1. 800

  2. 400

  3. 200

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

The box is a 20cm × 20cm × 20cm cube with volume 8000 cm³. Each pipe is a cylinder with length 10cm, radius 1cm, so volume = π(1)²(10) = 10π ≈ 31.4 cm³. If we could pack perfectly with no wasted space, maximum pipes = 8000/31.4 ≈ 255 pipes. However, cylindrical packing efficiency in a rectangular box is much less than 100% due to gaps between cylinders. Options A (800), B (400), and C (200) all assume unrealistic packing scenarios. The actual maximum is significantly less than 200, making 'None of these' the correct answer.