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

The volume of the sphere is 38808 cm³, find the curved surface area of the sphere.

  1. 5544 cm2

  2. 5045 cm2

  3. 4244 cm2

  4. 4345 cm2

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

Volume of sphere = (4/3)πr³ = 38808 cm³. Using π = 22/7, we get r³ = 38807 × 3/(4π) = 9261, so r = 21 cm. Curved surface area = 4πr² = 4 × (22/7) × 21² = 5544 cm². The formula relating volume and surface area of a sphere is CSA = 4πr² where r is derived from volume.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (Only quantity is to be considered) Sum of height and diameter of the cylinder is 22 meter. Quantity I :- Volume of the cylinder whose respective ratio of height to radius is 30 : 7 . Quantity II :- Volume of the cylinder if height of cylinder is 14 m .

  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 can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given h + d = 22m, and d = 2r, so h + 2r = 22. Quantity I: h/r = 30/7, so h = 30r/7. Substituting: 30r/7 + 2r = 22 gives 44r/7 = 22, so r = 3.5m and h = 15m. Volume I = π * 3.5² * 15 = 183.75π ≈ 577.3 m³. Quantity II: h = 14m, so d = 22 - 14 = 8m, r = 4m. Volume II = π * 4² * 14 = 224π ≈ 703.7 m³. Since 703.7 > 577.3, Quantity II > Quantity I.

Multiple choice

What is the Curved surface area of the conical temple ? Statement I : Height of the temple is 35 m. Statement II : Diameter of the base is 20 % more than the height of the temple. Statement III : Area of the base is 5544 sq. m.

  1. Only I and III

  2. Only I

  3. Only III

  4. Any of the two

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

To find CSA of a cone (πrl), we need radius and slant height. Statement I gives height (35m). Statement II gives diameter is 20% more than height, so diameter = 42m, radius = 21m. From I and II: l = √(35² + 21²) = √(1225 + 441) = √1665 ≈ 40.8m. From I and III: Base area πr² = 5544 gives r = 21m, then same slant height calculation. From II and III: From III, πr² = 5544 gives r = 21m; from II, diameter is 1.2×height, so height = 42/1.2 = 35m. Then l = √(35² + 21²). Any two statements together provide sufficient information.

Multiple choice

In a circular ground, a rectangular tank measures 130m × 110 m, if the area of the remaining part is 20350 m2 . So the radius of the field will be ?

  1. 95 m

  2. 115 m

  3. 118 m

  4. 105 m

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

Circular ground with rectangular tank. Rectangle area = 130 × 110 = 14300 m². Remaining area = 20350 m². Total circle area = 14300 + 20350 = 34650 m². Circle area = πr² = 34650, so r² = 34650/π ≈ 34650/3.14 ≈ 11035. r = √11035 ≈ 105 m. The radius is 105 meters.

Multiple choice

The length of the rectangle is 200% more than the width of the rectangle. If the its perimeter is 1440 mm Then find the area of the Rectangle ?
  1. $98900 mm2$
  2. $78200 mm2$
  3. $9720 cm2$
  4. $97200 mm2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Length is 200% more than width, so L = w + 2w = 3w. Perimeter P = 2(L+w) = 2(3w+w) = 8w = 1440, so w = 180 mm. Length L = 540 mm. Area = L × w = 540 × 180 = 97200 mm². Option C is wrong because it uses cm² not mm².

Multiple choice

From the four corners of a rectangular sheet of dimensions 25 cm \times 20 cm, square of side 2 cm is cut off from four corners and a box is made. The volume of the box is –
  1. $828 cm3$
  2. $672 cm3$
  3. $500 cm3$
  4. $1000 cm3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When squares of side 2 cm are cut from corners, the new dimensions of the box base become (25-4) = 21 cm and (20-4) = 16 cm. The height of the box is 2 cm (the side of the cut square). Volume = length × width × height = 21 × 16 × 2 = 672 cm³.

Multiple choice

The curved surface area of a cylindrical rod is 264 m2 and its volume is 924 m3. The ratio of its semi diameter to height is -

  1. 7: 6

  2. 7: 3

  3. 6: 7

  4. 3: 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a cylinder with curved surface area (CSA) = 2πrh = 264 and volume = πr²h = 924, dividing volume by CSA gives r/2 = 924/264 = 3.5, so r = 7. Substituting r = 7 in CSA: 2π(7)h = 264, we get h = 6. The ratio of semi-diameter (r) to height is 7:6. Option A correctly states this ratio.

Multiple choice

What would be the cost of laying a carpet on a floor which has its length and breadth in the ratio of 23: 12 and its perimeter 210 feet, if the cost per square feet of laying carpet is Rs. 4.50?

  1. Rs. 12178

  2. Rs. 11178

  3. Rs. 10178

  4. Rs. 14728

  5. Rs. 13178
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The length and breadth are 23x and 12x respectively. Perimeter = 2(23x + 12x) = 70x = 210, so x = 3. Area = 69 × 36 = 2484 sq ft. Cost = 2484 × 4.50 = Rs. 11178.

Multiple choice

What will be the side of rhombus if its area is 3000 square units and its one diagonal is 50 units ?
  1. $130$
  2. $65$
  3. $78$
  4. $104$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of rhombus = (d1 × d2)/2 where d1, d2 are diagonals. Given area = 3000 and d1 = 50, we get d2 = (2×3000)/50 = 120. Each diagonal divides the rhombus into 4 right triangles with legs (d1/2) = 25 and (d2/2) = 60. The side is the hypotenuse: sqrt(25² + 60²) = sqrt(625 + 3600) = sqrt(4225) = 65 units.

Multiple choice

(\text{There are two concentric circles with outer circle of radius 24 cm. If the area of the inner circles is one third of the area between the two circles, then find the ratio of the circumference of the outer circle to that of the inner circle.})
  1. $2 : 1$
  2. $3 : 1$
  3. $2 : 3$
  4. $3 : 2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let outer radius R=24 cm and inner radius r. Given inner area = 1/3 of area between circles: πr² = (1/3)π(R² - r²). Simplifying: 3r² = R² - r², so 4r² = R², giving r = R/2. Circumference ratio = 2πR/2πr = R/r = 2:1. Option A is correct.

Multiple choice

The diameters of two given circles are in the ratio 12 : 5 and the sum of their areas is equal to the area of a circle of diameter 65 cm. What are their radii?

  1. 12 cm and 5 cm

  2. 24 cm and 10 cm

  3. 60 cm and 25 cm

  4. 30 cm and 12.5 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let radii be 12k and 5k (diameter ratio 12:5). Sum of areas: π(12k)² + π(5k)² = π(144k² + 25k²) = 169πk². Target circle area: π(32.5)² = 1056.25π. Equating: 169k² = 1056.25, so k² = 6.25 and k = 2.5. Therefore radii are 12×2.5 = 30 cm and 5×2.5 = 12.5 cm. Note that options A and B show diameters, not radii.