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

Passage

Find the value of Q1 and Q2 and state the correct relationship.

Quantity I: Area of rectangle whose sides are in the ratio 3 : 1 and perimeter twice the circumference of a semi-circle with area 77 cm2. Quantity II: Curved surface area of a cylinder of radius 12 cm and height equal to the side of square of area 49 cm2.

  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: Semi-circle area 77 = (1/2)πr² gives r=7. Perimeter = πr+14 = 36. Rectangle perimeter=72. With sides ratio 3:1, sides are 27 and 9. Area = 243. Quantity II: Square area 49 gives side=7 (cylinder height). Cylinder CSA = 2πrh = 2π×12×7 = 528. Since 528 > 243, Quantity II is greater.

Multiple choice

Passage

In each of the following questions, a question & then two statements – I & II are given. You have to determine that the data provided in these statements is enough to answer the question or not. Study both the statement: निम्नलिखित प्रत्येक प्रश्न में एक प्रश्न और फिर दो कथन I और II दिए गए हैं। आपको यह निर्धारित करना है कि इन कथनों में प्रदान किया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों का अध्ययन करें:

What is the curved surface area of cylinder? बेलन का वक्र पृष्ठीय क्षेत्रफल कितना है? Statement I. The base area of the cylinder is 154 cm2. statement II. The volume of the cone is 1540 cm3 . कथन I बेलन के आधार का क्षेत्रफल 154 सेमी2 है। कथन II. शंकु का आयतन 1540 सेमी3 है।

  1. Only Statement I alone. केवल कथन I

  2. Only Statement II alone. केवल कथन II

  3. Both Statements I and II together. दोनों कथन I और II एक साथ

  4. Neither Statement I nor II is sufficient. न तो कथन I और न ही II पर्याप्त है।

  5. Either Statement I or II. या तो कथन I या II
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Curved surface area of cylinder = 2πrh, where r is radius and h is height. Statement I gives base area πr² = 154, so we can find r = 7 cm but gives no information about h. Statement II talks about volume of a CONE, not the cylinder - this is irrelevant information. Neither statement gives height, so neither is sufficient alone or together.

Multiple choice

Passage

Each of the questions below consists of a question and two statements I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: नीचे दिए गए प्रत्येक प्रश्न में एक प्रश्न और उसके नीचे दो कथन I और II दिए गए हैं। आपको यह तय करना है कि कथनों में दिया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों को पढ़िए और उत्तर दीजिए:

If C1 and C2 are the circumferences of the outer and inner circles respectively. What is Ratio of C1 : C2? यदि C1 और C2 क्रमशः बाहरी और आंतरिक वृत्तों की परिधि हैं। C1 : C2 का अनुपात क्या है? Statement I : The two circles are concentric. Statement II : The area of the ring is 2/3 the area of greater circle. कथन I : दो वृत्त संकेंद्रित हैं। कथन II: वलय का क्षेत्रफल बड़े वृत्त के क्षेत्रफल का 2/3 है।

  1. statement I is sufficient to answer the question. कथन I प्रश्न का उत्तर देने के लिए पर्याप्त है।

  2. statement II is sufficient to answer the question. कथन II प्रश्न का उत्तर देने के लिए पर्याप्त है।

  3. both statement I and II together are necessary to answer the question. प्रश्न का उत्तर देने के लिए कथन I और II दोनों एक साथ आवश्यक हैं।

  4. both statements I and II together are not sufficient to answer the question. कथन I और II दोनों मिलकर प्रश्न का उत्तर देने के लिए पर्याप्त नहीं हैं।

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

Statement II alone is sufficient. If the ring area is 2/3 of the greater circle's area, then the smaller circle's area is 1/3 of the greater circle. Since circumference is proportional to the square root of area (C = 2πr and A = πr²), the ratio C1:C2 = √(3):√(1) = √3:1. Statement I (concentric circles) only tells us about position, not size relationship, so it's insufficient alone.

Multiple choice

Passage

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़िए और उसके आधार पर मात्रा I और मात्रा II की तुलना कीजिए।

Quantity I : A sphere of diameter 13.4 cm is melted and cast into a right circular cone of height 26.8 cm. The radius of the base of the cone is ? Quantity II: 9 cm. मात्रा I : 13.4 सेमी व्यास वाले एक गोले को पिघलाकर 26.8 सेमी ऊंचाई वाले एक लंब वृत्तीय शंकु में ढाला जाता है। शंकु के आधार की त्रिज्या है ? मात्रा II: 9 सेमी

  1. Quantity : I > Quantity : II मात्रा : I > मात्रा : II

  2. Quantity : I ≥ Quantity : II मात्रा : I ≥ मात्रा : II

  3. Quantity : I < Quantity : II मात्रा : I < मात्रा : II

  4. Quantity : II ≥ Quantity : I मात्रा: II ≥ मात्रा: I

  5. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sphere volume = (4/3)π(6.7)³. Cone volume = (1/3)πr²(26.8). Equating: (4/3)π(6.7)³ = (1/3)πr²(26.8). Solving: r² = 4(6.7)³/26.8. Since 26.8 = 4 × 6.7, r² = 4(6.7)³/(4 × 6.7) = (6.7)², so r = 6.7 cm. Quantity I (6.7) < Quantity II (9). The key is simplifying the relationship between sphere diameter and cone height.

Multiple choice

Passage

Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer: नीचे दिए गए प्रत्येक प्रश्न में एक प्रश्न और उसके नीचे तीन कथन क्रमांक I, II और III दिए गए हैं। आपको यह तय करना है कि कथनों में दिया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। सभी कथनों को पढ़िए और उत्तर दीजिए:

What is the cost of flooring a rectangular hall? एक आयताकार हॉल को फर्श करने की लागत क्या है? Statement I: The difference between the length and breadth of the rectangle is 5 cm. Statement II: The perimeter of the rectangular hall is 40 cm Statement III: The cost of flooring 100 cm2 area is Rs. 1000. कथन I: आयत की लंबाई और चौड़ाई के बीच का अंतर 5 सेमी है। कथन II: आयताकार हॉल का परिमाप 40 सेमी है कथन III: 100 सेमी2 क्षेत्र के फर्श की लागत 1000 रुपये है।

  1. Either statement III alone or statements I and II together are sufficient. या तो अकेले कथन III या कथन I और II एक साथ पर्याप्त हैं।

  2. statement III is sufficient. कथन III पर्याप्त है।

  3. statement I and III is sufficient. कथन I और III पर्याप्त है।

  4. Statement I, II, and III together are sufficient. कथन I, II और III एक साथ पर्याप्त हैं।

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

All three statements are required. From I and II: length - breadth = 5 and perimeter = 2(l + b) = 40, we can solve for length and breadth. From III: cost per cm² = Rs. 1000 ÷ 100 = Rs. 10. Then total cost = area × rate = (l × b) × 10.

Multiple choice

Passage

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis.

Quantity I: Find the volume of the sphere, whose radius is 7 cm. Quantity II: Find the volume of the cone whose height and diameter is 7 cm and 14 cm respectively?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity II ≥ Quantity I

  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: Volume of sphere = (4/3)π × 7³ ≈ 1437 cm³. Quantity II: Cone has r = 7, h = 7. Volume = (1/3)π × 7² × 7 ≈ 359 cm³. 1437 > 359, so I > II.

Multiple choice

Passage

Each of the following questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer नीचे दिए गए प्रत्येक प्रश्न में एक प्रश्न और उसके नीचे दो कथन क्रमांक I और II दिए गए हैं। आपको यह तय करना है कि कथनों में दिया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों को पढ़िए और उत्तर दीजिए

Find the height of the cylinder. बेलन की ऊँचाई ज्ञात कीजिए। Statement I : The Curved surface area of the cylinder is 396 cm2 and the total surface area of the cylinder is 1628 cm2. Statement II : The radius of the cylinder is 0.5 cm more than the 3 times of the height of the cylinder. कथन I: बेलन का वक्र पृष्ठीय क्षेत्रफल 396 सेमी 2 है और बेलन का कुल पृष्ठीय क्षेत्रफल 1628 सेमी 2 है। कथन II: सिलेंडर की त्रिज्या सिलेंडर की ऊंचाई के 3 गुना से 0.5 सेमी अधिक है।

  1. Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the questions कथन I अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है लेकिन कथन II अकेले प्रश्नों का उत्तर देने के लिए पर्याप्त नहीं है

  2. Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question. कथन II अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है लेकिन केवल कथन I अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question. दोनों कथनों को मिलाकर प्रश्नों का उत्तर देना आवश्यक है, लेकिन इनमें से कोई भी कथन अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

  4. Either statement I or statement II by itself is sufficient to answer the question. या तो कथन I या कथन II अपने आप में प्रश्न का उत्तर देने के लिए पर्याप्त है

  5. Statements I and II taken together are not sufficient to answer the question. कथन I और II को मिलाकर
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a cylinder: CSA = 2πrh and TSA = 2πr(r+h). Given CSA = 396 and TSA = 1628. TSA - CSA = 2πr², so 1628 - 396 = 2πr², giving 1232 = 2πr². Using π = 22/7: r² = 1232 × 7 / 44 = 49, so r = 7 cm. From CSA = 2πrh: 396 = 2 × 22/7 × 7 × h, giving 396 = 44h, so h = 9 cm. Statement I alone is sufficient. Statement II gives r = 3h + 0.5, which cannot be used alone without additional information.

Multiple choice

Passage

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question.

Find the total surface area of cylinder. (i) The ratio of the total surface area to the curved surface area of the cylinder is 5 : 2. (ii) The difference of the radius of cylinder and the height of the cylinder is 7 cm.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area = 2*pi*r*(r+h). Curved surface area = 2*pi*r*h. (i) (r+h)/h = 5/2, so 2r + 2h = 5h, 2r = 3h. (ii) r - h = 7. We have a system of two equations with two variables, which is sufficient to find r and h, and thus the surface area.

Multiple choice

Passage

The following questions are accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the questions.

Find the volume of right angle cone ? (A) Curved surface area of cone 18π units and T.S.A. of cone 50% more than curved surface area. (B) Volume of cylinder of twice the radius as that of cone & √3 time the height as that cone is 324π cubic units.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the questions.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A gives CSA = 18pi and TSA = 1.5 * CSA = 27pi. Since TSA = CSA + pi*r^2, pi*r^2 = 9pi, r = 3. Using CSA = pi*r*l = 18pi, 3l = 18, l = 6. Height h = sqrt(l^2 - r^2) = sqrt(27) = 3*sqrt(3). Volume can be found. Statement B gives volume of a cylinder with double radius and sqrt(3) height, which allows finding the cone's dimensions. Both are sufficient.

Multiple choice

Passage

Directions (76-80): Read the data carefully and answer the question Neeraj have some toys which are in the form of different structures. These are cylindrical, conical, spherical. Other than solid conical structure, all two are of both types i.e. hollow as well as solid. - Volume of a conical toy is three times of the volume of a solid cylindrical toy while radius of a solid spherical toy is half than that the radius of a conical toy. Outer radius of hollow cylindrical toys is same as radius of solid spherical toy while average of outer radius and inner radius of hollow cylindrical toys is equal to radius of solid cylindrical toy. Height of cylindrical, conical and hollow cylindrical toys is same i.e. 14cm - Number of solid spherical toys is 20% of total number of toys Neeraj have. Number of hollow spherical toys is 150% more than number of conical toys. Ratio between number of solid cylindrical toys to number of conical toys is 3:2. Total number of hollow cylindrical toys is 40% of total number of toys Neeraj have and also 20 more than the total number of solid spherical toys Neeraj have. - Volume of a hollow spherical toy is 33,957 cm3 whose inner radius is half of its outer radius. Volume of a hollow spherical toy is 5.25 time of volume of conical toy.

Find the curved surface area of one hollow cylindrical toy? (in cm2)

  1. (a) 616

  2. (b) 1232

  3. (c) 924

  4. (d) 462

  5. (e) 1386
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

Directions: Study the following information carefully and answer the question. The total surface area of a solid cube is 10,584 cm 2 . A sphere of maximum radius is cut out from it. The sphere is cut into eight identical parts by three cuts (one cut along each axis) and the volume of each identical part is (4840 + X) cm 3 . The total surface area of the one identical part is (1720.5 + Y) cm 2 .

If one identical part of the sphere is melted to form 21 small solid cylinders, whose radius is 3.5 cm, then what is the height (in cm) of the solid cylinder?

  1. 4

  2. 6

  3. 8

  4. 10

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

Passage

Directions: On the basis of the given information, answer the question. A room with 1 door and 2 windows has 2 tables, 1 freezer and 1 almirah. The dimensions of the door, windows and the objects kept inside the room are given in the table. Sr. No. Object Length Breadth Height 1. Room 13 feet 12 feet 10 feet 2. Table 5 feet 4 feet 4 feet 3. Freezer 4 feet 3 feet 5 feet 4. Almirah 4 feet 3 feet 8 feet 5. Door 6 feet 3 feet 6. Window 4 feet 3 feet

Find the cost of painting of all surfaces of the almirah, if the cost of painting is Rs. 5 per square feet.

  1. Rs. 680

  2. Rs. 480

  3. Rs. 520

  4. Rs. 750

  5. Rs. 620
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of an almirah (rectangular prism) is 2*(lb + bh + lh). With dimensions 4, 3, 8 feet, the area is 2*(12 + 24 + 32) = 2*68 = 136 square feet. At Rs. 5 per square foot, the cost is 136 * 5 = 680.

Multiple choice

Passage

Directions: Based on the following information, answer the following question. On 9 th October, 2021, it rained heavily throughout the day over the city of Punjab. Mr. Deshraj observed that each of the raindrops which reached him was in the shape of a hemisphere surmounted by a cone of the same radius of 1.5 mm and the volume of one of such raindrop was 3.75π mm 3 . Deshraj collected the rainwater in a vessel having a capacity of 2355 cm 3 . (Use π = 3.14)

Find the curved surface area of a raindrop.

  1. 26 mm2

  2. 22 mm2

  3. 36 mm2

  4. 28 mm2

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

Volume = 3.75 * pi = 2/3 * pi * r^3 + 1/3 * pi * r^2 * h. r = 1.5. 3.75 = 2/3 * (1.5)^3 + 1/3 * (1.5)^2 * h. 3.75 = 2.25 + 0.75 * h. 1.5 = 0.75 * h => h = 2. CSA = 2 * pi * r^2 + pi * r * l. l = sqrt(r^2 + h^2) = sqrt(2.25 + 4) = 2.5. CSA = 2 * pi * 2.25 + pi * 1.5 * 2.5 = 4.5 * pi + 3.75 * pi = 8.25 * pi = 8.25 * 3.14 = 25.905, approx 26.

Multiple choice

Passage

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. (1) If Quantity I ≥ Quantity II (2) If Quantity I > Quantity II (3) If Quantity I < Quantity II (4) If Quantity I = Quantity II or the relationship cannot be established from the information given (5) If Quantity I ≤ Quantity II

A spherical ball of radius 3.5 cm is to be shipped in a rectangular container. The dimensions of the container are consecutive even numbers. Quantity I: The minimum volume of the container Quantity II: 960 cm3

  1. (1)

  2. (2)

  3. (3)

  4. (4)

  5. (5)
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: Read the data given below carefully and answer the question. The data shows the volume and dimensions (length, breadth, and height) of four cuboidal tanks: A, B, C, and D. The data also depicts the time taken to fill or empty the tanks by inlet pipes X, Y, and the outlet pipe Z. 1. The breadth of tank D is 14 m. Tank Data: Tank Volume (m³) Dimensions: L × B × H (m) Time taken by pipe X to fill (hours) Ratio of time taken by pipe Y to fill and pipe Z to empty A 3,600 20 × 15 × ---- 10 2 : 3 B ----- 25 × 12 × 12 3 : 2 C 4,500 ---- × 6 × 15 18 1 : 4 D 16,800 14 × ---- × ---- ----- 3 : 5

Find the respective ratio of the lateral surface area of tank A to the total surface area of tank C.

  1. 5 : 4

  2. 2 : 5

  3. 7 : 15

  4. 7 : 19

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

Lateral surface area of tank A (20x15xH) = 2*H*(20+15) = 70H. Volume = 3600 = 20*15*H, so H = 12. LSA = 70*12 = 840. Total surface area of C (L*6*15) = 2*(6L + 90 + 15L) = 2*(21L + 90). Volume = 4500 = L*6*15, so L = 50. TSA = 2*(21*50 + 90) = 2*(1050 + 90) = 2280. Ratio = 840 / 2280 = 84 / 228 = 7 / 19.