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

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. What is the radius of the sphere? I. The cost of painting the surface area is Rs. 20 per m2. II. The sphere was formed by melting a cube of side 2 m.

  1. The question can be answered by using statement I alone, but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone, but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using either of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives the cost of painting, which requires knowing the surface area, but doesn't provide enough info to find the radius without knowing the total cost or surface area. Statement II provides the volume of the cube (2^3 = 8), which equals the volume of the sphere (4/3 * pi * r^3 = 8). This allows solving for r. Thus, II alone is sufficient.

Multiple choice

Directions: In this question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. The ratio of the total surface area of a cone to the curved surface area of the cone is 13 : 10. Quantity 1: Curved surface area of the cone if the sum of the radius and the slant height of the cone is 13 cm Quantity 2: Curved surface area of the cone if the radius of the cone is 6 cm

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 1 < Quantity 2

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area = pi*r*(r+l) and curved surface area = pi*r*l. Ratio (r+l)/l = 13/10 implies 10r + 10l = 13l, so 10r = 3l or l = (10/3)r. Quantity 1: r+l=13, so r + (10/3)r = 13 => (13/3)r = 13 => r=3, l=10. CSA = pi*3*10 = 30pi. Quantity 2: r=6, so l = (10/3)*6 = 20. CSA = pi*6*20 = 120pi. 30pi < 120pi.

Multiple choice

Directions: In the given question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. The volume of a solid sphere is 38,808 cm3. Quantity 1: The curved surface area of a cylinder in cm2, if the radius of the cylinder is 50% of the radius of the solid sphere and the height of the cylinder is 16 cm Quantity 2: 45% of the curved surface area of a cone in cm2, if the radius of the cone is the same as the radius of the solid sphere and the height of the cone is 28 cm

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

The ratio of the total surface area of a closed cylindrical vessel to the curved surface area of the same cylindrical vessel is 4 : 3 and the height of the cylindrical vessel is 14 cm more than the radius of the cylindrical vessel. Two cylindrical vessels of this type are filled up to 75% of their capacity with water. The total water from these cylindrical vessels is transferred into a number of small cylindrical vessel whose height is 2/3 of the original cylindrical vessel and the radius is one fourth of the original cylindrical vessel. Find the number of the small cylindrical vessels.

  1. 24

  2. 28

  3. 32

  4. 36

  5. 45
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total surface area (2*pi*r*(r+h)) to curved surface area (2*pi*r*h) is (r+h)/h = 4/3. Given h = r + 14, we get (r + r + 14)/(r + 14) = 4/3, leading to 6r + 42 = 4r + 56, so 2r = 14, r = 7, h = 21. Volume of one vessel is pi * 7^2 * 21 = 1029 * pi. Total water from two vessels is 2 * 0.75 * 1029 * pi = 1543.5 * pi. Small vessel volume is pi * (7/4)^2 * (21 * 2/3) = pi * 49/16 * 14 = 42.875 * pi. Number of vessels = 1543.5 / 42.875 = 36.

Multiple choice

(\text{The area of the ring is } 418 \text{ cm}^2\text{ . If the radius of the smaller circle is 6 cm. The radius of the bigger circle is-})

  1. 18 cm.

  2. 16 cm.

  3. 13 cm.

  4. 10 cm.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of ring = π(R² - r²) where R is radius of larger circle, r is radius of smaller circle. Given π(R² - 6²) = 418, so R² - 36 = 418/π ≈ 133. Therefore R² ≈ 169 and R = 13 cm. Option A (18 cm) is incorrect. Option B (16 cm) would give area ≈ 678, not 418. Option D (10 cm) is too small.

Multiple choice

A copper wire which lengths is 36 m. and diameter 2 mm, melted in the form of a sphere. Find the radius of sphere.

  1. 2.5 cm.

  2. 3 cm.

  3. 3.5 cm.

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

Copper wire is cylindrical. Length = 36 m = 3600 cm, diameter = 2 mm, so radius = 1 mm = 0.1 cm. Volume = πr²h = π × 0.01 × 3600 = 36π cm³. This forms a sphere with volume (4/3)πR³ = 36π, so R³ = (36π × 3)/(4π) = 27, R = 3 cm. Option B is correct because the sphere's radius calculates to 3 cm.

Multiple choice

Find the area and circumference of a circle of radius 35 cm.

  1. 3650 cm2, 210 cm

  2. 3250 cm2, 140 cm

  3. 3450 cm2, 216 cm

  4. 3650 cm2, 220 cm

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

For a circle with radius 35 cm: Area = πr² = (22/7) × 35² = (22/7) × 1225 = 22 × 175 = 3850 cm². Circumference = 2πr = 2 × (22/7) × 35 = 2 × 22 × 5 = 220 cm. The correct answer is 3850 cm² and 220 cm, which doesn't match any of the given options A-D.

Multiple choice

The length of a rectangle is 15 cm. which is 6 cm. less than the diameter of a circle. What is the area of circle?

  1. 346.5 sq.cm

  2. 173.25 sq.cm.

  3. 156 sq.cm.

  4. 132 sq.cm.

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

Length of rectangle = 15cm. This is 6cm less than circle's diameter, so diameter = 15 + 6 = 21cm. Radius = 10.5cm. Area = πr² = (22/7) × 10.5² = (22/7) × 110.25 = 22 × 15.75 = 346.5 sq.cm. The distractor 173.25 comes from using radius = 10.5 instead of squaring it properly.

Multiple choice

Find out the cost of painting a 16 m long square room at the rate of Rs. 5.50 per square meter. Statements: (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

The room is 16m long (given in question). To paint walls, we need the total wall area minus door/window area. Statement I gives width = 15m, so floor area = 16 × 15. Statement II gives height = 12m, so wall area = perimeter × height = 2(16 + 15) × 12 = 744 m². Statement III gives door/window area = 60 m² to be subtracted. Paintable area = 744 - 60 = 684 m². Cost = 684 × 5.50 = Rs. 3762. All three statements are necessary.