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

From a cylindrical log of wood of 10 cm radius and 35 cm length, a cone of 8 cm radius and 14 cm height is cut out. What is the maximum possible volume of a cylinder that can be cut out from the remaining solid?

  1. 4400 cm3

  2. 6600 cm3

  3. 5500 cm3

  4. 6400 cm3

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

The remaining solid is a cylinder of radius 10 and length 35 minus a cone. The maximum cylinder that can be cut from the remaining space depends on the dimensions of the cavity. Given the geometry, 6600 cm^3 is the calculated maximum.

Multiple choice

If a rectangular block (4 × 4 × 10) inches is placed inside a right circular cylinder of radius 3 inches and height 10 inches, the volume of the unoccupied portion of the cylinder is how many cubic inches?

  1. (6π - 16) cubic inches

  2. 60π cubic inches

  3. (160π - 30) cubic inches

  4. (90π - 160) cubic inches

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

The volume of the cylinder is pi * r^2 * h = pi * 3^2 * 10 = 90pi. The volume of the rectangular block is 4 * 4 * 10 = 160. The unoccupied volume is 90pi - 160.

Multiple choice

Ramesh bought a decorative item made of some kind of wood consist of a cylindrical body, hemisphere and a cone. What is the ratio of the volume of cone, hemisphere and cylinder if they all have same height and radius?

  1. 2 : 1 : 3

  2. 1 : 3 : 2

  3. 2 : 3 : 1

  4. 1 : 2 : 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of cone = (1/3)pi*r^2*h. Volume of hemisphere = (2/3)pi*r^3. Volume of cylinder = pi*r^2*h. Since h=r, volumes are (1/3)pi*r^3, (2/3)pi*r^3, pi*r^3. Ratio = 1/3 : 2/3 : 1 = 1 : 2 : 3.

Multiple choice

The area of a playground is 1600 m2. What is the perimeter? Statement I: It is a perfect square playground. Statement II: It costs Rs. 3200 to put a fence around the playground at the rate of Rs. 20 per metre.

  1. I alone sufficient while II alone not sufficient to answer

  2. II alone sufficient while I alone not sufficient to answer

  3. Either I or II alone sufficient to answer

  4. Both I and II are necessary to answer
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area = 1600. If it is a square, side = 40, perimeter = 160. Statement II gives total cost 3200 and rate 20, so perimeter = 3200/20 = 160. Both statements independently provide the perimeter.

Multiple choice

A hemispherical dome rests on its circular base. A cylinder is placed inside the dome with one of its bases resting on the base of the dome. Find the radius of the largest possible cylinder that can be placed, if the radius of the hemisphere is 10√(3/2)

  1. 8

  2. 10

  3. 9

  4. 11
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a cylinder of radius r and height h inside a hemisphere of radius R, the relationship is r^2 + h^2 = R^2. To maximize volume V = pi * r^2 * h, we find that the optimal radius is R * sqrt(2/3). Given R = 10 * sqrt(3/2), r = 10 * sqrt(3/2) * sqrt(2/3) = 10.

Multiple choice

A solid wooden toy is in the form of a cone mounted on a hemisphere. If the radii of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of wood used in the toy.

  1. 343.72 cm3

  2. 266.11 cm3

  3. 532.22 cm3

  4. 133.55 cm3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius = 4.2 cm. Hemisphere volume = (2/3) * pi * 4.2^3 = 155.19. Cone height = 10.2 - 4.2 = 6 cm. Cone volume = (1/3) * pi * 4.2^2 * 6 = 110.84. Total = 155.19 + 110.84 = 266.03. Option B is the closest.