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 curved surface area of a closed cylinder is 225 cm2 and the area of its base is 169 cm2, then find the total surface area of the cylinder.
  1. $394 cm2$
  2. $343 cm2$
  3. $563 cm2$
  4. $195 cm2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Curved surface area = 2πrh = 225π. Base area = πr² = 169π, so r = 13 cm. From curved surface area: 2π(13)h = 225π, giving h = 225/26 ≈ 8.65 cm. Total surface area = 2πr(h + r) = 2π(13)(225/26 + 13) = 26π(225/26 + 338/26) = 26π(563/26) = 563π cm².

Multiple choice

The radius of a hemisphere is 6.3 cm. What will be its volume?

  1. 572.80 cm3

  2. 643.50 cm3

  3. 523.90 cm3

  4. 353.38 cm3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of hemisphere = (2/3)πr³. Given r = 6.3 cm. Volume = (2/3) × 3.14159 × (6.3)³ = (2/3) × 3.14159 × 250.047 ≈ 523.9 cm³. Option C matches this calculation. (6.3)³ = 250.047, multiplied by π/1.5 gives approximately 523.90.

Multiple choice

Perimeter of a rectangle is 2 cm more than circumference of a circle and area of circle is 1386 cm2. If breadth of rectangle is equal to radius of circle, then find length of rectangle (in cm )? एक आयत का परिमाप एक वृत्त की परिधि से 2 सेमी अधिक है और वृत्त का क्षेत्रफल 1386 सेमी2 है। यदि आयत की चौड़ाई वृत्त की त्रिज्या के बराबर है, तो आयत की लंबाई (सेमी में) ज्ञात करें?

  1. 40 cm 40 सेमी

  2. 42 cm 42 सेमी

  3. 44 cm 44 सेमी

  4. 46 cm 46 सेमी

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

Circle area = πr² = 1386, so r² = 1386/π = 1386/22 × 7 = 441, r = 21 cm. Circle circumference = 2πr = 2 × 22/7 × 21 = 132 cm. Rectangle perimeter = 132 + 2 = 134 cm. Rectangle breadth = r = 21 cm. So 2(length + 21) = 134, length + 21 = 67, length = 46 cm.

Multiple choice

A tent is of a shape of right circular cylinder up to a height of 4 meters and then becomes a right circular cone with maximum height of 52 meters above the base. If the radius of the base is 14 meters, then what is the cost of covering the inner side of the tent at the rate of Rs 4.5 per square meter? एक तम्बू 4 मीटर ऊपर तक बेलनाकार है और फिर एक शंकु बन जाता है यदि तम्बू की अधिकतम ऊचाई 52 मीटर है तथा आधार की त्रिज्या 14 मीटर है, तो तंबू के अंदरूनी हिस्से को 4.5 रुपये प्रति वर्ग मीटर की दर से ढकने के लिए लागत क्या आएगी?

  1. Rs. 11994 / 12884 रु.

  2. Rs. 15484 / 15484 रु

  3. Rs. 11484 / 11484 रु.

  4. Rs. 8484 / 8484 रु
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The tent consists of a cylinder (height 4m, radius 14m) and a cone (height 48m, radius 14m). Inner surface area = CSA of cylinder + CSA of cone = 2πrh + πrl = 2×(22/7)×14×4 + (22/7)×14×50 = 352 + 2200 = 2552 m². At Rs 4.5 per m², total cost = 2552 × 4.5 = Rs 11484. The slant height of cone l = √(48² + 14²) = 50m.

Multiple choice

(\text{In the following questions, two quantities are given as Quantity I and Quantity II. Find the correct relationship among them.}\\text{Quantity I:}\text{ Area of the square is 7200 cm}^2\text{ which is four times the area of the rectangle whose length and breadth is in the ratio of 9:8. What is the sum of length and breadth of the rectangle? }\\text{Quantity II:}\text{ A rectangular water tank is 300 cm} \times 488 \text{cm is dug inside a circular field. The area of the remaining portion is 12000cm}^2\text{ . Find the radius of the circular field.})

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Square area = 7200 = 4 × rectangle area, so rectangle area = 1800. Length:Breadth = 9:8, let dimensions be 9x and 8x. Then 72x² = 1800, x² = 25, x = 5. Length = 45, breadth = 40. Sum = 85. Quantity II: Tank area = 300 × 488 = 146400. Circular field area = 146400 + 12000 = 158400. πr² = 158400, r² = 158400/π ≈ 50414, r ≈ 224.5. Since 224.5 > 85, Quantity II > Quantity I.

Multiple choice

What is the total cost of painting a cone at the rate of Rs.60 per square metre? Statement I: The radius and the slant height of the flask are 21 m and 16 m respectively Statement II: The area of the base of cone is 616 sq. m and its height is 14 m.

  1. If the data in statement I alone is sufficient to answer the question.

  2. If the data in statement II alone is sufficient to answer the question.

  3. If the data either in statement I alone or statement II alone are sufficient to answer the question.

  4. If the data given in both I and II together are not sufficient to answer the question.

  5. If the data in both the statements I and II together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the painting cost, we need the total surface area of the cone. Statement I gives radius 21 m and slant height 16 m, so curved surface area = pi × 21 × 16 = 336pi sq.m, and cost = 336pi × 60 = Rs. 20,160pi. Statement II gives base area 616 sq.m, so radius = sqrt(616/pi) = 14 m, and height 14 m, giving slant height = sqrt(14² + 14²) = 14√2 m. Then curved surface area = pi × 14 × 14√2 = 196pi√2 sq.m, and cost can be calculated. Each statement alone provides sufficient data to determine the cost.

Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. $Quantity I: area of a rectangle is (84m^2) and its perimeter is (38m). If a (2m) wide path is constructed both side along with the longer side of the rectangle then find the area of the path?$ $Quantity II: the volume of cylinder is (192). Find the volume of another cylinder which height is same to the first and radius is half?$

  1. Quantity I < Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or Relation cannot be establish
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Rectangle with area 84 and perimeter 38. Using l×w=84 and 2(l+w)=38, we get l=14, w=6. A 2m path along both longer sides creates additional area unclear without diagram - could be path along outside or inside. Quantity II: V₁ = πr²h = 192, V₂ = π(r/2)²h = πr²h/4 = 48. Without clear path configuration, relationship cannot be established.

Multiple choice

The question given below has few statements along with it. You have to determine which of the statements are sufficient for answering the question and mark your answer accordingly: What will be the cost of painting the four walls and the roof of a room with length, width and height as 7 m, 5m and 2.5 meters respectively? The room has one door and two windows. Statement I. Cost of painting per square meter Statement II. Area of window is half of the area of the floor.

  1. If statement 1 alone is sufficient

  2. If statement 2 alone is sufficient

  3. If either 1 or 2 alone is sufficient

  4. If both the statements together are necessary

  5. If both the statements even together are not sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement II gives area of window = half of floor area = (1/2) × 35 = 17.5 sq m. But we don't know how many windows total or their individual areas. Statement I gives cost per sq m but without total area to paint, this is useless. Even together, we're missing: door area, exact window configuration, and we don't know if painting excludes door/window openings. The information is fundamentally incomplete. Option E is correct.

Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values.\n\n\textbf{Quantity I:} The length of a rectangular park is 56.25% more than its breadth. There is a fountain in it of area 625 square meter and which is one fourth of the total area of the park. What is the perimeter of the park?\n\textbf{Quantity II:} The ratio of length to breadth of the rectangle is 5: 3. If the length of the rectangle is decreased by 8 m it becomes a square, then what is the area of the square thus formed?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can’t be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Park area = 625 × 4 = 2500 sq m. Length = 1.5625 × breadth, so 1.5625b² = 2500, b = 40 m, L = 62.5 m, Perimeter = 2(62.5 + 40) = 205 m. Quantity II: 5x - 8 = 3x gives x = 4, square side = 12 m, Area = 144 sq m. Note: Perimeter (m) and area (sq m) are dimensionally different - you cannot directly compare them. However, the question asks to compare numerical values 205 vs 144, and numerically 205 > 144.

Multiple choice

$A metallic cylinder and a metallic cone are melted to form a solid sphere. Radius of cylinder and cone are in the ratio 3: 2 respectively. What is the radius of sphere? (Take (\pi = \frac{22}{7})$ Statement I: Height of cylinder and cone are in the ratio 4: 5 respectively and sum of volume of cylinder and cone is 39424 cm3. Statement II: Volume of cone is 27104 cm3 less than the volume of cylinder and sum of their heights is 54 cm. Statement III: Curved surface area of cylinder is 3168 cm2 and its radius and height are in the ratio 7: 8 respectively.

  1. Only statement I alone is sufficient

  2. Either statement II alone is sufficient or statement I and III together are sufficient.

  3. Either statement I alone is sufficient or statement II and III together are sufficient.

  4. Any of the two statements together are sufficient/

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

Statement I alone is sufficient because it provides the height ratio (4:5), radius ratio (3:2 given), and total volume (39424 cm³). Using volume formulas V = πr²h (cylinder) and V = (1/3)πr²h (cone), we can set up equations to solve for the actual radii and heights, then equate total volume to sphere volume (4/3)πR³. Statement II and III together also work: II gives volume difference and height sum, III gives curved surface area and radius:height ratio for the cylinder.

Multiple choice

In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option: Quantity I: The perimeter of a rectangular park is 192 m. If the length of the park is 56 m then find the cost of cleaning the entire area of the park at Rs. 9 per m^2. Quantity II: The radius and the height of a cylindrical tank are 21 m and 17 m, respectively. If the cost of filling 1m3 of water in the tank is Rs. 0.85, then find the cost required to fill the tank completely.

  1. Quantity I < Quantity II

  2. Quantity I > Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: Perimeter = 192 means 2(l+b) = 192, l+b = 96. With l=56, b=40. Area = 56×40 = 2240 m². Cost = 2240 × 9 = Rs 20,160. Quantity II: Volume = πr²h = π×21²×17 ≈ 23569 m³. Cost = 23569 × 0.85 ≈ Rs 20,033. So Quantity I (20,160) > Quantity II (20,033). Answer B is correct.

Multiple choice

Following questions consist a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question or not. निम्नलिखित प्रश्न में एक प्रश्न और दो कथन I और II दिए गए हैं, आपको यह तय करना होगा कि कथन में दिए गए डेटा प्रश्न का उत्तर देने के लिए पर्याप्त हैं या नहीं। What is the volume of an equilateral prism? (I) Radius of the sphere of the maximum size that can be placed in this prism is 12 cm. (II) Height of the prism is 18 cm. एक समबाहु प्रिज्म का आयतन क्या है? (I) इस प्रिज्म में रखे जा सकने वाले अधिकतम आकार के गोले की त्रिज्या 12 सेमी है। (II) प्रिज्म की ऊँचाई 18 सेमी है।

  1. Only II केवल II

  2. Only I केवल I

  3. Both from I and II I और II दोनों से

  4. Any one of the two दोनों में से कोई एक

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

For an equilateral prism, the maximum sphere radius equals the triangle's inradius. From Statement I: inradius = 12cm, so triangle height = 12√3 cm, giving base side and area. From Statement II: height = 18cm directly gives volume calculation. Either statement alone suffices. Option D is correct.

Multiple choice

In each of the following questions, a question is followed by two statements numbered I and II. Read both the statements and answer accordingly. नीचे दिए गए प्रत्येक प्रश्न में, एक प्रश्न और उसके बाद दो कथन I और II दिए गए हैं। आपको निर्णय लेना है कि कथन में दिया गया डाटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। What is the total cost of painting a cone at the rate of Rs.60 per square metre? Statement I: The radius and the slant height of the flask are 21 m and 16 m respectively Statement II: The area of the base of cone is 616 sq. m and its height is 14 m. 60 रुपये प्रति मी2. की दर से शंकु को पोलिश करने की कीमत क्या होगी| कथन I: शंकु की त्रिज्या और त्रियर्क ऊँचाई क्रमशः 21 मी. और 16 मी. है| कथन II: शंकु के आधार का क्षेत्रफल 616 मी2. तथा ऊँचाई 14 मी. है|

  1. If the data in statement I alone is sufficient to answer the question. यदि कथन I में दिया गया डाटा अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है

  2. If the data in statement II alone is sufficient to answer the question. यदि कथन II में दिया गया डाटा अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है

  3. If the data either in statement I alone or statement II alone are sufficient to answer the question. यदि या तो कथन I में दिया गया डाटा अकेले या कथन II में दिया गया डाटा अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है

  4. If the data given in both I and II together are not sufficient to answer the question. यदि कथन I और II मिलाकर प्रश्न का उत्तर देने के लिए पर्याप्त नहीं हैं

  5. If the data in both the statements I and II tog
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: radius r=21m, slant height l=16m. Lateral surface area = πrl = π×21×16. Note: l