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 sphere of diameter 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 6 cm. If the sphere is completely submerged in water, then by how much will the surface level of water be raised?

  1. 0.5 cm

  2. 1 cm

  3. 1.5 cm

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

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 3^3 = 36 * pi. Volume of displaced water in cylinder = pi * R^2 * h = pi * 6^2 * h = 36 * pi * h. Equating volumes: 36 * pi = 36 * pi * h => h = 1 cm.

Multiple choice

A hemispherical bowl of internal radius 18 cm contains a liquid. The liquid is filled in small cylindrical bottles of internal radius 3 cm and internal height 4 cm. What is the number of bottles used to empty the bowl?

  1. 54

  2. 81

  3. 108

  4. 135
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of bowl = (2/3) * pi * R^3 = (2/3) * pi * 18^3 = (2/3) * pi * 5832 = 3888 * pi. Volume of bottle = pi * r^2 * h = pi * 3^2 * 4 = 36 * pi. Number of bottles = (3888 * pi) / (36 * pi) = 108.

Multiple choice

A cone of height 16 cm and diameter 14 cm is mounted on a hemisphere of same diameter. What is the volume of the solid thus formed? (Take π = 22 7 )

  1. 1,540 cm3

  2. 1,078 cm3

  3. 1,048 cm3

  4. 770 cm3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume = Volume of cone (1/3 * pi * r^2 * h) + Volume of hemisphere (2/3 * pi * r^3). With r = 7 and h = 16: V = (1/3 * 22/7 * 49 * 16) + (2/3 * 22/7 * 343) = (22 * 7 * 16 / 3) + (44 * 49 / 3) = 2464/3 + 2156/3 = 4620/3 = 1540.

Multiple choice

Directions : Select the correct alternative from the given choices. Two circles, C1 and C2, each of radius 3 cm, with centres at X and Y respectively, intersect each other such that the line XY joining the centres intersects the circles C1 and C2 at P and Q respectively and PQ = 2 cm. lf the whole assembly is enclosed in a rectangle of minimum possible area, the perimeter of the rectangle is

  1. 28 cm

  2. 32 cm

  3. 40 cm

  4. 60 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The distance between centers XY = 3+3-2 = 4 cm. The rectangle width is 2 * radius = 6 cm. The length is 2 * radius + XY = 6 + 4 = 10 cm. Perimeter = 2 * (6 + 10) = 32 cm.

Multiple choice

Directions : Select the correct alternative from the given choices. Raghu wants to construct a circular swimming pool in his plot which is in the shape of a trapezium. The lengths of the oblique sides of the plot are 26 m and 30 m. lf the radius of the biggest circle that can be marked for the pool is 12 m, what must be the minimum area (in sq.m) of the plot?

  1. 336

  2. 672

  3. 728

  4. 1344
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The circle is inscribed in the trapezium. The height of the trapezium is the diameter of the circle, which is 24 m. Using the properties of a tangential trapezium, the area can be calculated.

Multiple choice

Directions : Answer the questions independently of each other. A cube is completely filled with water. 50% of the water in the cube is used to fill 90% of the volume of a sphere of radius Rs. 75% of the remaining water in the cube fills 60% of the volume in a cone with its height equal to its base radius Ro and the balance water left in the cube after this is used to fill 30% of a cylinder with its height equal to one-third its base radius Rc. Then, Rs3: Ro3: Rc3 =

  1. 3 : 15 : 10

  2. 10 : 27 : 30

  3. 10 : 45 : 9

  4. 2 : 9 : 6

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

Let cube volume be V. 0.5V = 0.9 * (4/3)pi*Rs^3. 0.75 * 0.5V = 0.6 * (1/3)pi*Ro^3. 0.125V = 0.3 * pi*Rc^2*(Rc/3) = 0.1 * pi*Rc^3. Solving for ratios of cubes leads to 2:9:6.

Multiple choice

The volume of a cylinder is 5500 cm3. If its curved surface area is 4400 sq. cm, find its height.

  1. 380 cm

  2. 480 cm

  3. 180 cm

  4. 280 cm

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

Dividing the volume formula (pi * r^2 * h = 5500) by the curved surface area formula (2 * pi * r * h = 4400) gives r / 2 = 5 / 4, which simplifies to r = 2.5 cm. Substituting r = 2.5 cm back into the curved surface area equation yields 2 * (22/7) * 2.5 * h = 4400, which solves to h = 280 cm.

Multiple choice

Directions: Select the correct alternative from the given choices. The ratio of the curved surface areas of two cylinders A and B is 2 : 3. If the ratio of the volumes of A and B is 4 : 5, find the ratio of the heights of A and B.

  1. 2/3

  2. 5/9

  3. 1/3

  4. 2/5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved surface area S = 2*pi*r*h and volume V = pi*r^2*h. The ratio of areas is (r1*h1) / (r2*h2) = 2/3. The ratio of volumes is (r1^2*h1) / (r2^2*h2) = 4/5. Dividing the volume ratio by the area ratio gives (r1/r2) = (4/5) / (2/3) = 6/5. Substituting r1/r2 into the area ratio: (6/5) * (h1/h2) = 2/3, so h1/h2 = (2/3) * (5/6) = 10/18 = 5/9.