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

A cone of height 9 cm. with diameter of its base 18 cm. is carved out from a wooden soiled sphere of radius 9 cm. The percentage of the wood wasted is - 9 सेमी. ऊँचाई के शंकु के आधार का व्यास 18 सेमी. है, 9 सेमी. त्रिज्या वाले लकड़ी के ठोस गोले में से निकाला जाता है तो नष्ट हुई लकड़ी का प्रतिशत क्या है?

  1. 50%

  2. 25%

  3. 40%

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

Volume of cone = (1/3)πr²h = (1/3)π × 9² × 9 = 243π cubic cm. Volume of sphere = (4/3)πr³ = (4/3)π × 9³ = 972π cubic cm. Wood wasted = (Volume of sphere - Volume of cone) / Volume of sphere × 100 = (972π - 243π) / 972π × 100 = 729/972 × 100 = 75%. The cone carved out uses only 25% of the sphere's volume, leaving 75% as waste.

Multiple choice

The respective ratio of curved surface area and total surface area of a cylinder is 4:5. If the curved surface area of the cylinder is (1232 cm^2), What is the height?

  1. 14 cm

  2. 28 cm

  3. 7 cm

  4. 56 cm

  5. 24 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a cylinder, curved surface area (CSA) = 2πrh and total surface area (TSA) = 2πr(r + h). Given CSA:TSA = 4:5, so 2πrh / 2πr(r+h) = 4/5. Simplifying: h/(r+h) = 4/5, so 5h = 4r + 4h, giving h = 4r. With CSA = 1232 = 2πrh = 2πr(4r) = 8πr². Solving: r² = 1232/(8π) ≈ 49, so r = 7. Height h = 4r = 28 cm. Option B is correct.

Multiple choice

If the four equal circles of diameter is 6 meter touch each other externally, then find the area of the region bounded by the four circles.

  1. (35 - 9π) m2

  2. (36 - 8π) m2

  3. (36 - 9π) m2

  4. (25 - 9π) m2

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

When four equal circles (diameter 6m, so radius 3m) touch each other externally, their centers form a square of side 6m. The area bounded by the circles is the area of this square minus the four quarter-circles (which together form one full circle). Square area = 36 m², Circle area = π × 3² = 9π m². Therefore, bounded region area = 36 - 9π m².

Multiple choice

A tent is of the shape of a right circular cylinder up to a height of 3 metres and then becomes a right circular cone with maximum height of 13.5 metres above the ground. If the radius of the base is 14 metres, the cost of painting the inner side of the tent at the rate of Rs. 2 per square metre is-

  1. Rs. 2050

  2. Rs. 2060

  3. Rs. 2068

  4. Rs. 2080
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area to paint = CSA of cylinder + CSA of cone. Cylinder: 2πrh = 2 × π × 14 × 3 = 84π. For the cone, slant height l = √(h² + r²) = √(10.5² + 14²) = √306.25 = 17.5m. CSA = πrl = π × 14 × 17.5 = 245π. Total area = 329π ≈ 1034 m². Cost = 1034 × 2 = Rs. 2068.

Multiple choice

Find the correct relationship between the given quantities: Quantity I: Value of ‘x’. A cylinder having height 196 cm and radius 14 cm is casted into ‘x’ number of cubes having side 7 cm. Quantity II: Find the height of the cone in cm (approximately).Curved surface area of a right circular cone is 176 m2 and its base diameter is 1400 cm.

  1. Quantity II > Quantity I

  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
A Correct answer
Explanation

Quantity I: Cylinder volume = π × 14² × 196 = π × 196 × 196 = 38416π cm³. Cube volume = 7³ = 343 cm³. Number of cubes x = 38416π/343 ≈ 112π ≈ 352. Quantity II: Cone diameter = 1400 cm = 14 m, so radius = 7 m. CSA = πrl = 176, so π × 7 × l = 176, giving l = 176/(7π) ≈ 8 m. Height h = √(l² - r²) = √(64 - 49) = √15 ≈ 3.87 m = 387 cm. Quantity II ≈ 387 > Quantity I ≈ 352. Option A is correct.

Multiple choice

Following question consists 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. What is the cost of the flooring rectangular hall? (I) The ratio of length and breadth of the hall is 3 : 4. (II) Difference of diagonal and perimeter of the hall is 36 cm and cost of flooring is Rs 15 per square meter.

  1. Only II

  2. Only I

  3. I and II

  4. Any one of the two.

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

Statement I alone gives only ratio (3:4), insufficient for area or cost. Statement II: Let dimensions be l and b. Diagonal = sqrt(l^2 + b^2), Perimeter = 2(l+b). Difference = 36. Combined with ratio 3:4, we can solve: let l=3x, b=4x. Diagonal = 5x, Perimeter = 14x, 14x-5x=9x=36, so x=4. Area = 12×16 = 192 sq cm. Both statements needed. Answer C is correct.

Multiple choice

The total surface area of a solid cylinder is 462 cm². The area of curved surface is 1/3 of the total surface area. The volume of cylinder is – एक ठोस बेलन का सम्पूर्ण पृष्ठ क्षेत्रफल 462 सेमी2 है । इसका वक्रपृष्ठ क्षेत्रफल सम्पूर्ण पृष्ठ क्षेत्रफल का 1/3 है । बेलन का आयतन है –

  1. 530 cm³/सेमी.³

  2. 536 cm³/सेमी.³

  3. 539 cm³/सेमी.³

  4. 545 cm³/सेमी.³
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area = 462 cm². Curved surface = (1/3) × 462 = 154 cm². So top + bottom = 462 - 154 = 308 cm². Each circular face area = 308/2 = 154 = πr², giving r = 7 cm. Curved surface = 2πrh = 154, so 2π × 7 × h = 154, giving h = 3.5 cm. Volume = πr²h = π × 49 × 3.5 = 539 cm³ (taking π = 22/7).

Multiple choice

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio (1: 1 : 8: 27: 27). What is the respective ratio of the total surface area of given five cubes to the surface area of the formed cube?

  1. 3 : 4

  2. 4 : 3

  3. 3 : 2

  4. 2 : 3

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

When a cube is melted and recast, volume is conserved. The side lengths of cubes are proportional to the cube root of their volumes. Given volume ratio 1:1:8:27:27, the side ratio is 1:1:2:3:3. Surface area of a cube is proportional to the square of its side. Summing the surface areas of all five cubes and comparing to the original cube's surface area yields the ratio 3:2.

Multiple choice

The ratio of the curved surface area to the total surface area of a cylinder is 3 : 5. Find out the volume of the cylinder if the curved surface is 462 cm2. (π = 22/7)

  1. 1228

  2. 1723

  3. 1540

  4. 1617

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

CSA:TSA = 3:5 means 2πrh:2πr(r+h) = 3:5, so h:(r+h) = 3:5, giving 5h = 3r + 3h, so h = 1.5r. Given CSA = 462, so 2πrh = 462. Substituting h = 1.5r: 2πr(1.5r) = 462. Using π = 22/7: r = 7 cm, h = 10.5 cm. Volume = πr²h = (22/7) × 49 × 10.5 = 1617 cm³.

Multiple choice

A hollow cylindrical iron pipe of length 1.4 m has bore radius 2.5 cm and thickness of the metal is 1 cm. What is the volume of the iron used in the pipe?

  1. 2640 cm3

  2. 2604 cm3

  3. 2460 cm3

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

For a hollow cylinder, the volume of material = π(R² - r²)h, where R is outer radius, r is inner radius (bore radius). Inner radius = 2.5 cm. Thickness = 1 cm, so outer radius = 2.5 + 1 = 3.5 cm. Length = 1.4 m = 140 cm. Volume = π[(3.5)² - (2.5)²] × 140 = π[12.25 - 6.25] × 140 = π(6) × 140 = 840π ≈ 2638.9 cm³. Rounding gives approximately 2640 cm³. Option B has incorrect digit order, while option C has different values.

Multiple choice

The volume of a box with a square base is 54 cubic centimeters. If the height of the box is twice the width of the base, what is the height, in centimeters? वर्ग आधार वाले बॉक्स का आयतन 54 घन सेंटीमीटर है। यदि बॉक्स की ऊंचाई आधार की चौड़ाई की दोगुनी है, तो सेंटीमीटर में ऊंचाई क्या है?

  1. 3

  2. 4

  3. 6

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

Let base width = x, then height = 2x. Volume of box = base area × height = x² × 2x = 2x³ = 54. Solving: x³ = 27, so x = 3. Height = 2x = 6 cm. The distractor 3 comes from confusing width with height, while 9 would result from using height = x².

Multiple choice

A right circular cone is 8 cm. high and the radius of the base is 2 cm. The cone is melted and recast in to a sphere. The diameter of the sphere is -

  1. 8 cm.

  2. 6 cm.

  3. 4 cm.

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

Volume of cone = (1/3)πr²h = (1/3)π(2²)(8) = (32/3)π cm³. When melted and recast, volume remains constant. Volume of sphere = (4/3)πr³. Equating: (4/3)πr³ = (32/3)π, which gives r³ = 8, so r = 2 cm. Therefore diameter = 4 cm.