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 square hole of cross - sectional area $4\displaystyle cm^{2}$ is drilled across a cube with its length parallel to a side of the cube. If edge of the cube measures $5 cm$, what is the total surface area of the body so formed?
  1. $140 cm^{2}$
  2. $142 cm^{2}$
  3. $162 cm^{2}$
  4. $182 cm^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of cube = 6 * 5^2 = 150. When a hole is drilled, we lose two faces of area 4, but gain the internal surface area of the hole. Internal area = perimeter * length = 4 * sqrt(4) * 5 = 4 * 2 * 5 = 40. Total = 150 - 2*4 + 40 = 182.

Multiple choice

The curved surface area and volume of a cylindrical pillar are $264 m^2$ and $924 m^{3}$. Find the ratio of its diameter to its height.
  1. $3 : 7$
  2. $7 : 3$
  3. $6 : 7$
  4. $7 : 6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CSA = 2 * pi * r * h = 264. Volume = pi * r^2 * h = 924. Dividing V by CSA: (pi * r^2 * h) / (2 * pi * r * h) = r / 2 = 924 / 264 = 3.5. So r = 7. Then 2 * pi * 7 * h = 264 => h = 264 / (44) = 6. Diameter = 14, height = 6. Ratio 14:6 = 7:3.

Multiple choice

The height of a right circular cylinder is $6 m$. If three times the sum of the areas of its two circular faces is twice the area of the curved surface, then the radius of the base is
  1. $4 m$
  2. $3 m$
  3. $2 m$
  4. $1 m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let r be the radius and h = 6. The area of two circular faces is 2 * pi * r^2. The curved surface area is 2 * pi * r * h. The problem states 3 * (2 * pi * r^2) = 2 * (2 * pi * r * 6). Simplifying gives 6 * pi * r^2 = 24 * pi * r. Dividing by 6 * pi * r (assuming r is not 0) gives r = 4.

Multiple choice

A hollow right circular cylinder with height $8$ cm and base radius $7$ cm is opened out into a rectangle. What are the length and breadth of the rectangle respectively ?
  1. $22$ cm, $16$ cm
  2. $44$ cm , $8$ cm
  3. $22$ cm, $8$ cm
  4. $44$ cm, $16$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a cylinder is opened into a rectangle, the height of the cylinder becomes one side of the rectangle (8 cm) and the circumference of the base becomes the other side. The circumference is 2 * pi * r = 2 * 3.14 * 7 = 44 cm (using pi approx 22/7).

Multiple choice

Sixteen cylindrical cans each with a radius of $1$ unit are placed inside a cardboard box four in a row. If the cans touch the adjacent cans and or the walls of the box, then which of the following could be the interior area of the bottom of the box in square units?
  1. $16$
  2. $32$
  3. $64$
  4. $128$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

16 cans, 4 in a row. This means a 4x4 grid of cans. Each can has radius 1, so diameter 2. The box must be 4*2 = 8 units wide and 4*2 = 8 units long. Area = 8 * 8 = 64.

Multiple choice

From a cuboidal cardboard box of dimensions $80\;cm\times40\;cm\times15\;cm,\;6$ circles of radius $7\;cm$ were cut out from the front face. Find the surface area of the remaining box.
  1. $9176\;cm^2$
  2. $9066\;cm^2$
  3. $9776\;cm^2$
  4. $9076\;cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of cuboid = 2(lb + bh + lh) = 2(80*40 + 40*15 + 80*15) = 2(3200 + 600 + 1200) = 10000. Area removed = 6 * (pi * r^2) = 6 * (22/7) * 49 = 6 * 22 * 7 = 924. Remaining area = 10000 - 924 = 9076 cm^2.

Multiple choice

From a closed cardboard cylinder of height $30\;cm$ and diameter of base $21\;cm,\;15$ rectangles of size $2\;cm\times1.5\;cm$ are cut out. Find the total surface area of the remaining cylinder.
  1. $1628\;cm^2$
  2. $2528\;cm^2$
  3. $2618\;cm^2$
  4. $2628\;cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total surface area of cylinder = 2*pi*r*(r+h). Diameter = 21, so r = 10.5. Area = 2 * (22/7) * 10.5 * (10.5 + 30) = 66 * 40.5 = 2673. Area of 15 rectangles = 15 * (2 * 1.5) = 45. Remaining area = 2673 - 45 = 2628.