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

What is the cost of flooring a rectangular room? Statement I: The ratio of length and breadth of the room is 5:4. Statement II: The length of the room is 50 meters and the cost of flooring is Rs.1000 per square meter. Statement III: The perimeter of the room is 180 meters and the cost of flooring is Rs.1000 per square meter.

  1. Only I and II

  2. Only II and III

  3. Any two of the three

  4. Only I and III

  5. I and either II or III
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find flooring cost, we need area and rate. Rate Rs.1000/sqm is in both II and III. Using I+II: length 50m, ratio 5:4 gives breadth 40m, area 2000 sqm. Using I+III: perimeter 180m with 5:4 ratio gives length 50m, breadth 40m, area 2000 sqm. Using II+III: length 50m with perimeter 180m gives breadth 40m. All pairs yield cost = 2000 × 1000 = Rs.20,00,000.

Multiple choice

If the diameter of a circle is decreased by 50%, find the percentage decrease in its area. यदि एक वृत्त के व्यास में 50% की कमी की जाती है, इसके क्षेत्रफल में प्रतिशत कमी ज्ञात कीजिए।

  1. 50%

  2. 100%

  3. 65%

  4. 75%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If diameter decreases by 50%, the radius also decreases by 50%. Area = πr². If new radius = 0.5r, new area = π(0.5r)² = 0.25πr² = 25% of original. This represents a 75% decrease. Many students incorrectly think 50% diameter decrease means 50% area decrease.

Multiple choice

What would be the cost of fencing of a rectangle whose length is 20% more than its breadth and area of rectangle is (900 m^2)?\

  1. Rs. 380

  2. Rs. 400

  3. Rs. 415

  4. Rs. 450

  5. Cannot be determine
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

From area=900m² and length=1.2×breadth, we get breadth²=750 and perimeter=2(length+breadth)=120.5m. However, the cost per meter of fencing is not given, making it impossible to calculate the total cost. Without this information, the answer cannot be determined.

Multiple choice

The curved surface area of a cylindrical pole is 528 m2 and its volume is 1848 m3. Find the ratio of radius to height? यदि एक बेलनाकार खम्भे के वक्रपृष्ठ का क्षेत्रफल 528 मी.2 है तथा इसका आयतन 1848 मी.3 है तो उस बेलनाकार खम्भे की त्रिज्या तथा ऊँचाई का अनुपात ज्ञात कीजिए।

  1. 7 : 9

  2. 7 : 12

  3. 14 : 9

  4. 12 : 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CSA = 2πrh = 528, so h = 12/r. Volume = πr²h = 1848. Substituting h gives πr²(12/r) = 1848, so πr(12) = 1848, giving r = 7. Then h = 12/7, so r:h = 7:12. The ratio of radius to height is 7:12.

Multiple choice

The height of right circular cylinder is increased by 50% and radius is decreased by 30% then find the change in volume of cylinder? एक लम्बवृत्तीय बेलन की ऊँचाई को 50% बढ़ा दिया जाए तथा त्रिज्या 30% कम कर दी जाए तो आयतन पर क्या प्रभाव पड़ेगा?

  1. increased by 26.5% / बढ़ेगा

  2. Decreased by 26.5% / घटेगा

  3. Increased by 24.5% / बढ़ेगा

  4. Decreased by 24.5% / घटेगा
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original volume V = πr²h. New h' = 1.5h, new r' = 0.7r. New volume V' = π(0.7r)²(1.5h) = π × 0.49r² × 1.5h = 0.735πr²h = 0.735V. Change = (0.735 - 1) × 100 = -26.5%. Volume decreases by 26.5%.

Multiple choice

The radius of a sphere 9 cm. it is melted and cast into wire of radius 0.3 cm. Find the length of wire एक गोले की त्रिज्या 9 सेमी. है। उसे पिघलाकर एक तार बनाया जाता है, जिसकी त्रिज्या 0ण्3 सेमी. है तो तार की लम्बाई ज्ञात कीजिए।

  1. 0.8 metre/मीटर

  2. 324 metre/मीटर

  3. 810 metre/मीटर

  4. 108 metre/मीटर
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = (4/3)π(9)^3 = 972π cm³. Volume of cylinder (wire) = π(0.3)²h. Equating volumes: π(0.09)h = 972π, so h = 972/0.09 = 10,800 cm = 108 m. The wire radius 0.3 cm must be used correctly in the calculation.

Multiple choice

The slant height of a conical tent is 2.6 meter and the area of curved surface is 2.6 π m.2 . Find the volume of conical tent. किसी शंक्वाकार तम्बू की ऊँचाई 2.6 मी. है और उसके वक्रपृष्ठ का क्षेत्रफल 2.6π मी2 है तो उसका आयतन ज्ञात कीजिए।

  1. 0.8π

  2. 1.8π

  3. 1.6π

  4. 2.4π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The curved surface area of a cone is πrl, where r is radius and l is slant height. Given πrl = 2.6π and l = 2.6m, we get r = 1m. Using l² = r² + h², the height h = 2.4m. Volume of a cone = (1/3)πr²h = (1/3)π(1)²(2.4) = 0.8π cubic meters. Note: Hindi text uses ऊँचाई (height) incorrectly; the 2.6m given is actually slant height based on the calculation.

Multiple choice

A cylinder of maximum possible volume is made by solid cube. How much approximate percentage volume is lost in this process? एक घन से अधिकतम आयतन का बेलन बनाया जाता है। इस प्रक्रिया में लगभग कितने प्रतिशत आयतन नष्ट होगा ?

  1. 33.33%

  2. 20.1%

  3. 16.66%

  4. 21.4%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a cube of side a, max volume cylinder has diameter = side and height = side. V_cylinder = π(a/2)²a = πa³/4 ≈ 0.785a³. V_cube = a³. Volume lost = a³ - πa³/4 = a³(1 - π/4) ≈ a³(1 - 0.785) = 0.215a³. Percentage lost = 21.5%. The answer 21.4% is approximately correct.

Multiple choice

The area of a floor to be carpeted is 50 square meters. Find the width of the carpet? I. The total cost of carpeting is Rs. 5000. II. The length of the carpet is 10 m. III. The width of carpet is equal to that of the floor.

  1. Only I

  2. Only II

  3. Only III

  4. Only I and II

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

Given: floor area = 50 sq m. Statement II: carpet length = 10 m. If width = 5 m, then carpet area = 50 sq m, which matches floor area. Statement II alone is sufficient to deduce width = 5 m (assuming carpet covers floor fully). Statement I gives cost but not dimensions. Statement III says widths are equal but doesn't give value.

Multiple choice

How many solid spherical balls can be formed from a solid cylinder 18 c.m. high and with radius of 10 centimeter, each ball being 6 centimeter in diameter? 18 सेंटीमीटर ऊंचाई और 10 सेंटीमीटर त्रिज्या वाले ठोस बेलन से, कितने ठोस गोलाकार गेंदों को बनाया जा सकता है, जिसमे प्रत्येक गेंद 6 सेंटीमीटर व्यास में है ?

  1. 500

  2. 200

  3. 50

  4. 150
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cylinder volume = π × 10² × 18 = 1800π cm³. Each ball radius = 3 cm, volume = (4/3)π(3)³ = 36π cm³. Number of balls = 1800π/36π = 50.

Multiple choice

The ratio of volumes of two sphere is 8: 27.The difference between the radius of first sphere and second sphere is 3 cm. What is the ratio of total surface area of these sphere respectively? दो गोलों के आयतन का अनुपात 8: 27 है। पहले गोले के त्रिज्या और दूसरे गोले की त्रिज्या में अंतर 3 सेमी है इन गोलों के कुल सतह क्षेत्रफल का अनुपात क्रमशः क्या है?

  1. 2 : 3

  2. 9 : 4

  3. 8 : 27

  4. 4 : 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume ratio V1/V2 = (r1/r2)³ = 8/27, so r1/r2 = 2/3. Given r2 - r1 = 3 cm. If r1 = 2k and r2 = 3k, then 3k - 2k = k = 3, so r1 = 6, r2 = 9. Surface area ratio = 4πr1² : 4πr2² = r1² : r2² = 6² : 9² = 36 : 81 = 4 : 9 after simplification.

Multiple choice

The area of a square is 196 sq. cm. Its side is half the radius of a circle. The circumference of the circle is equal to the breadth of a rectangle. If perimeter of the rectangle is 712 cm, what is the length of the rectangle? एक वर्ग का क्षेत्रफल 196 वर्ग सेमी. है। इसकी भुजा वृत्त की त्रिज्या की आधी है। वृत्त की परिधि आयत की चौड़ाई के बराबर है। यदि आयत का परिमाप 712 सेमी. है, आयत की लम्बाई क्या है?

  1. 196 cm. /सेमी.

  2. 186 cm. /सेमी.

  3. 180 cm. /सेमी.

  4. 190 cm. /सेमी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Square area = 196 sq. cm, so side = √196 = 14 cm. Circle radius = 2 × 14 = 28 cm. Circumference = 2πr = 2 × (22/7) × 28 = 176 cm (this is rectangle's breadth). For rectangle: perimeter = 2(length + breadth) = 712 cm, so length = (712/2) - 176 = 356 - 176 = 180 cm. The π = 22/7 convention simplifies to a clean integer answer.

Multiple choice

A solid metallic prism whose area of base is 126 cm2 and height is 77cm is melted and recast in the shape of a cone if the radius and height of cone is equal then find the radius of cone. एक ठोस धात्विक प्रिज्म जिसके आधार का क्षेत्रफल 126 सेमी2 और ऊचाई 77 सेमी. है ,को पिघलाकर उसे पुनः एक शंकु के आकार में ढाला जाता है ,जिसकी आधार त्रिज्या और ऊचाई बराबर है। तो शंकु की त्रिज्या ज्ञात कीजिये ।

  1. 21 cm/सेमी.

  2. 14 cm/सेमी.

  3. 28 cm/सेमी.

  4. 3.5 cm/सेमी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of prism = Base area × height = 126 × 77 = 9702 cm³. This equals volume of cone = (1/3)πr²h. Given r = h for the cone, so (1/3)πr³ = 9702. Using π = 22/7: (1/3)(22/7)r³ = 9702, giving r³ = 9702 × 21/22 = 441 × 21 = 9261. Therefore r = ³√9261 = 21 cm. Option A matches. The key is equating volumes and using r = h.