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 ratio of curved surface areas of the frustums of two cones is 2 : 3 and the ratio of their slant heights is 8 : 3, then the ratio of sum of the radii of the frustums of the 1st cone to that of the 2nd cone is

  1. 2 : 1

  2. 1 : 2

  3. 4 : 1

  4. 1 : 4

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

The curved surface area of a frustum is pi * (r1 + r2) * l. Given the ratio of areas is 2:3 and slant heights is 8:3, we have (r1a + r2a) * 8 / ((r1b + r2b) * 3) = 2/3. Solving for the ratio (r1a + r2a) / (r1b + r2b) gives 2/3 * 3/8 = 6/24 = 1/4.

Multiple choice

If a cylindrical vessel of 50 m diameter and height of 36 m holds liquid chemical 120 times a hemispherical bowl holds, find the radius of the hemispherical bowl.

  1. 6.55 m

  2. 13.10 m

  3. 19.65 m

  4. 25.55 m

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

Cylinder volume = pi * r^2 * h = pi * 25^2 * 36 = 22500 * pi. Hemispherical bowl volume = (2/3) * pi * R^3. 120 * (2/3) * pi * R^3 = 22500 * pi. 80 * R^3 = 22500. R^3 = 281.25. R = cube root of 281.25 approx 6.55.

Multiple choice

Find the curved surface area of a cylinder if the radius of the cylinder is twice the radius of a cone whose curved surface area is 110 m2 and the latent height is 7 m. Also, height of the cylinder is equal to that of cone. (Take approximate values.)

  1. 298 m2

  2. 300 m2

  3. 305 m2

  4. 308 m2

  5. 316 m2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The cone radius is 110 divided by pi times 7, which is approximately 5 m. Its height is sqrt(7^2 - 5^2), approximately 4.9 m, so the cylinder radius is about 10 m. Its curved surface area is approximately 2pi times 10 times 4.9 = 308 m^2.

Multiple choice

The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.

  1. 3.2 cm

  2. 1.6 cm

  3. 2.56 cm

  4. 5.6 cm

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

Volume of two cones = 2 * (1/3 * pi * r^2 * h). Sum = 1/3 * pi * (1.6)^2 * (4.3 + 2.1) = 1/3 * pi * 2.56 * 6.4 = 5.4613 * pi. Sphere volume 4/3 * pi * R^3 = 5.4613 * pi. R^3 = 4.096, so R = 1.6. Diameter = 3.2 cm.

Multiple choice

A right circular cylinder is partially filled with water. Two iron spherical balls are completely immersed in the water so that the height of the water in the cylinder rises by 4 cm. If the radius of one ball is half of the other and the diameter of the cylinder is 18 cm, then the radii of the spherical balls are

  1. 6 cm and 12 cm

  2. 4 cm and 8 cm

  3. 3 cm and 6 cm

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

Volume of water rise = pi * r^2 * h = pi * 9^2 * 4 = 324pi. Volume of two spheres = 4/3 * pi * (r^3 + (2r)^3) = 4/3 * pi * 9r^3 = 12pi * r^3. 12pi * r^3 = 324pi => r^3 = 27 => r = 3. Radii are 3 cm and 6 cm.