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 height of a given cone be doubled and radius of base remains the same, the ratio of the volume of the given cone to that the second cone will be - यदि दिये गये शंकु की ऊँचाई को दोगुना कर दिया जाए तथा त्रिज्या समान रहे तो दिये गये शंकु का आयतन और दूसरे शंकु के आयतन के मध्य अनुपात होगा-

  1. 8 : 1

  2. 2 : 1

  3. 1 : 2

  4. 1 : 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cone V = (1/3)πr²h. For first cone: V₁ = (1/3)πr²h. For second cone (height doubled, radius same): V₂ = (1/3)πr²(2h) = 2V₁. The ratio V₁:V₂ = 1:2. This tests understanding that volume is directly proportional to height when radius is constant, since V ∝ h.

Multiple choice

Find the height of the cylinder. I. The Curved surface area of the cylinder is 396 cm² and the total surface area of the cylinder is 1628 cm². II. The radius of the cylinder is 0.5 cm more than the 3 times of the height of the cylinder.

  1. Only I

  2. Only II

  3. Both together are sufficient

  4. Both together are not sufficient

  5. Any one is sufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From Statement I: Curved Surface Area (CSA) = 2πrh = 396, and Total Surface Area (TSA) = 2πr(r+h) = 1628. Since TSA = CSA + 2πr², we get 1628 = 396 + 2πr², giving 2πr² = 1232. This allows finding r. With r known, CSA = 2πrh = 396 gives h = 396/(2πr). Statement I alone is sufficient. Statement II relates r and h but gives no numerical values, making it insufficient alone. Option A is correct.

Multiple choice

A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is 1/4th of its height. Find the surface area of the solid.

  1. 680 sq. cm

  2. 800 sq. cm

  3. 770 sq. cm

  4. 720 sq. cm

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

Total length = cylinder height + 2 × radius = 35 cm. Given diameter = height/4, so 2r = h/4, meaning h = 8r. Therefore: 8r + 2r = 35, so 10r = 35 and r = 3.5 cm. Height h = 28 cm. Surface area = curved surface of cylinder + surface of sphere = 2πrh + 4πr² = 2π × 3.5 × 28 + 4π × 3.5² = 196π + 49π = 245π ≈ 770 sq. cm.

Multiple choice

If the volume of a cylinder of height 56 cm. is equal to the volume of the cube of 11 cm. side, then find the radius of the base of the cylinder.

  1. 2.25 cm.

  2. 2.5 cm.

  3. 2.75 cm.

  4. 3.25 cm.

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

Volume of cube with side 11 cm = 11³ = 1331 cm³. Volume of cylinder = πr²h = πr² × 56. Equating: πr² × 56 = 1331. Solving: r² = 1331/(56π) ≈ 1331/175.93 ≈ 7.56. Therefore: r ≈ √7.56 ≈ 2.75 cm.

Multiple choice

The radius and the height of a cone are in the ratio 4:3. What will be the ratio of the curved surface area and total surface area of the cone? एक शंकु की त्रिज्या तथा ऊँचाई का अनुपात 4 : 3 है। तदनुसार उसकी वक्राकार सतह के क्षेत्रफल तथा कुल सतह के क्षेत्रफल का अनुपात कितना होगा?

  1. 5:9

  2. 3:7

  3. 5:4

  4. 16:9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given r:h = 4:3, the slant height l forms a 3-4-5 triangle, so l = 5. CSA = πrl = πr(5), TSA = πr(r+l) = πr(4+5) = 9πr. Ratio CSA:TSA = 5πr:9πr = 5:9.

Multiple choice

There are two concentric circles of radius 14 cm. and 7 cm respectively. Find the area between two concentric circles. क्रमशः 14 सेमी. और 7 सेमी. त्रिज्या के दो वृत्त हैं दोनों संकेन्द्रीय वृत्तों के बीच का क्षेत्रफल ज्ञात कीजिए।

  1. 616 cm2/सेमी2

  2. 462 cm2/सेमी2

  3. 154 cm2/सेमी2

  4. 654 cm2/सेमी2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area between circles = π(R² - r²) where R = 14, r = 7. Area = π(14² - 7²) = π(196 - 49) = π(147). Using π = 22/7: Area = (22/7) × 147 = 22 × 21 = 462 cm².

Multiple choice

There is a square room of area 100 sq. m. The centre of the room is covered by a square carpet and the rest of the floor is covered by oil cloths. The carpet and the cloths cost Rs.18 and Rs.7.5 per square metre respectively and the total cost of the carpet and oil cloth is Rs.1422. Find the width of the oil cloth.

  1. 1 m.

  2. 2 m.

  3. 2.5 m.

  4. 0.5 m.

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

Room area is 100 sq m, so side length is 10 m. Let carpet side = x. Then carpet area = x² and oil cloth area = 100 - x². The cost equation: 18x² + 7.5(100 - x²) = 1422. Solving: 10.5x² = 672, so x² = 64 and x = 8 m. The oil cloth borders the carpet on all sides, so its width = (10 - 8)/2 = 1 m. Option A is correct.

Multiple choice

What is the cost of painting the walls of a rectangular room? I. Length, breadth and height of the room are in the ratio 3 : 2 : 1. II. Length of the room is equal to the side of the square whose area is 2304 m2 and cost of painting the walls is Rs. 85 per sq. m. III. Breadth of the room is equal to the height of the triangle whose base is 8 m. and area is 128 m2 and cost of painting the walls is Rs. 85 per sq. m.

  1. I and II

  2. I and III

  3. Only III

  4. I and either II or III

  5. Any two of the three
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the ratio but not actual dimensions. Statement II gives length via square area and painting rate. Statement III gives breadth via triangle area and repeats painting rate. We need I plus either II or III to get all dimensions and cost information.

Multiple choice

In each of the following question a question is followed by three statements. Study the question and the statements and decide the information given in which of the statements (s) is/are necessary to answer the question? Find out the cost of a painting at the rate of Rs. 5.50 per square meter of 16 m. long square room? (I) The width of the room is 15 m. (II) The height of the room is 12 m. (III) The total area of the door and window is 60 m².

  1. Only II

  2. All I, II and III

  3. Only I and II

  4. Only II and III

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

To find the painting cost, we need the total wall area minus door/window area. Wall area = 2 × length × height + 2 × width × height = 2(16×12) + 2(15×12) = 384 + 360 = 744 m². Paintable area = 744 - 60 = 684 m². Cost = 684 × 5.50 = Rs. 3762. All three statements I, II, and III are necessary - length and width to calculate perimeter, height for wall dimensions, and door/window area for deductions.

Multiple choice

What is the cost of painting the two adjacent walls of a rectangular hall which has no windows or doors? A. The area of the base of the hall is 24 sq. meters. B. The breadth, length and the height of the hall are in the ratio of 4: 6: 5. C. Area of one wall is 30 square meters.

  1. Only A and B

  2. Only B

  3. Only C

  4. Either A or C

  5. Data inadequate
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Painting cost requires cost per unit area. A gives only floor area. B gives ratios but no dimensions. C gives wall area but not which wall. Even combining all, we don't know cost per square meter or which two adjacent walls to paint. Data is inadequate.

Multiple choice

Find the value of Q1 and Q2 and state the correct relationship.\nQuantity 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.\nQuantity 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: Rectangle sides in ratio 3:1. Let sides be 3x and x. Perimeter = 2(3x + x) = 8x. Semi-circle with area 77 = (1/2)πr² gives r² = 49/π, r = 7/√π. Circumference = πr + 2r = π(7/√π) + 2(7/√π) = 7√π + 14/√π. Perimeter of rectangle = twice this = 14√π + 28/√π. So 8x = 14√π + 28/√π. Area = 3x² = 3[(14√π + 28/√π)/8]². This is complex. Let me recalculate: semi-circle area 77 means (πr²)/2 = 77, so r² = 154/π ≈ 49, so r ≈ 7. Semi-circle circumference (including diameter) = πr + 2r ≈ 7π + 14 ≈ 36. Rectangle perimeter = 2 × 36 = 72. So 8x = 72, x = 9. Rectangle area = 3x × x = 3 × 81 = 243. Quantity II: Square with area 49 has side 7. Cylinder height = 7, radius = 12. CSA = 2π × 12 × 7 = 168π ≈ 528. Since 528 > 243, Quantity II is greater.

Multiple choice

Radius of a cone is decreased by 40% whereas its height is decreased by 50%. Find the ratio of their volumes. शंकु के त्रिज्या में 40% की कमी की गयी जबकि इसकी ऊंचाई में 50% की कमी की गई है। उनके आयतन का अनुपात ज्ञात कीजिये।

  1. 25:4

  2. 50:9

  3. 27:8

  4. 51:25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original volume of cone = (1/3)πR²H. After 40% decrease, new radius = 0.6R. After 50% decrease, new height = 0.5H. New volume = (1/3)π(0.6R)²(0.5H) = (1/3)π(0.18R²H). Therefore ratio original:new = 1:0.18 = 50:9. The calculation correctly applies the percentage decreases to both dimensions.

Multiple choice

A hollow cylinder of height 3 cm,is recasted into a solid cylinder of height 9cm. If the external and internal radii of the hollow cylinder are 4.3 cm and 1.1 cm respectively.What will be the radius of the solid cylinder?

  1. 2.8 cm.

  2. 2.4 cm.

  3. 3.2 cm.

  4. 4.8 cm.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a shape is recast, its volume remains constant. Volume of hollow cylinder = π(R² - r²)h = π(4.3² - 1.1²) × 3 = π(18.49 - 1.21) × 3 = π × 17.28 × 3. Volume of solid cylinder = πR² × 9. Equating: πR² × 9 = π × 51.84, giving R² = 5.76, so R = 2.4 cm.

Multiple choice

The curved surface of a cylinder is 1000 cm2 .A wire of diameters 5 mm. is wound around it ,so as to cover it completely .What is the length of the wire used? एक बेलन का वक्रपृष्ठ 1000 सेमी2 है। एक 5 मिमी. व्यास वाले तार को इसके चारों ओर लपेटा जाता है। जिसमें यह इसकी पूरी तरीके से ढ़क ले। प्रयोग हुये तार की लम्बाई क्या है?

  1. 22 m.

  2. 20 m.

  3. 18 m.

  4. 34 m.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cylinder curved surface area = 2πrh = 1000 cm². Wire diameter = 5mm = 0.5cm, so circumference of each turn = πd = 0.5π cm. Length of wire = CSA / wire diameter = 1000 / 0.5 = 2000 cm = 20m. The wire winds around the cylinder with its diameter as the effective spacing. Option A (22m), C (18m), and D (34m) are incorrect calculations.

Multiple choice

Find the value of quantities and state the correct relationship. ( \text{A hemisphere of radius 4 cm is to be shipped in a shipping box of rectangular shape. The dimension of the box are consecutive odd numbers.} ) ( \text{Quantity I: Minimum volume of box required to have the shipment possible.} ) ( \text{Quantity II: 960 cm}^3 )

  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
A Correct answer
Explanation

Quantity I: The hemisphere radius is 4 cm, so its minimum bounding box must have dimensions at least 8 cm x 8 cm x 4 cm (diameter x diameter x height). With consecutive odd dimensions, the smallest such box is 7 x 9 x 11 or 9 x 11 x 13. Testing 9x11x13: volume = 1287 cm³, which is > 960 cm³. Therefore Quantity I > Quantity II.