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

An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of each of cone and cylinder is $8 /cm$. The cylindrical part is $240 \ cm$ high and the conical part is $36 \ cm$ high. Find The volume of iron used
  1. $50688{ cm }^{ 3 }$
  2. $42652{ cm }^{ 3 }$
  3. $50878{ cm }^{ 3 }$

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

Volume = Volume of cylinder + Volume of cone. V = pi * r^2 * h_cyl + (1/3) * pi * r^2 * h_cone. V = pi * 8^2 * 240 + (1/3) * pi * 8^2 * 36 = 15360 * pi + 768 * pi = 16128 * pi. Using pi = 3.14, V = 50641.92. The provided answer 50688 assumes pi = 22/7.

Multiple choice

The internal and external radii of a metallic spherical shell are $4$ cm and $8$ cm, respectively. It is melted and recast into a solid right circular cylinder of height $9\displaystyle \frac{1}{3} $ cm. Find the diameter of the base of the cylinder.
  1. $16$ cm
  2. $18$ cm
  3. $12$ cm
  4. $14$ cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of spherical shell = (4/3) * pi * (R^3 - r^3) = (4/3) * pi * (8^3 - 4^3) = (4/3) * pi * (512 - 64) = (4/3) * pi * 448. Cylinder volume = pi * r_c^2 * h = pi * r_c^2 * (28/3). Equating them: (4/3) * 448 = r_c^2 * (28/3). r_c^2 = (4 * 448) / 28 = 64. r_c = 8. Diameter = 2 * r_c = 16 cm.

Multiple choice

If the radius of a right circular cylinder open at both the ends is decreased by $25\%$ and the height of the cylinder is increased by $25\%$, then the surface area of the cylinder thus formed is:

  1. Remains unaltered
  2. Increases by $25\%$
  3. Decreases by $25\%$
  4. Decreases by $6.25 \%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of a cylinder is 2 * pi * r * h. If r becomes 0.75r and h becomes 1.25h, the new area is 2 * pi * (0.75r) * (1.25h) = 0.9375 * (2 * pi * r * h). This is a decrease of 1 - 0.9375 = 0.0625, which is 6.25 percent.

Multiple choice

The ratio between the radius of the base and height of the cylinder is $2:3$. If the volume is $12936 cm^{3}$, what is the total surface area of the cylinder?
  1. $3080 cm^{2}$
  2. $3000 cm^2$
  3. $4000 cm^2$
  4. $4050 cm^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

r:h = 2:3, so r=2k, h=3k. Volume = pi*r^2*h = (22/7)(4k^2)(3k) = 12936. (264/7)k^3 = 12936. k^3 = 12936 * 7 / 264 = 343. k = 7. r=14, h=21. Total Surface Area = 2*pi*r(r+h) = 2*(22/7)14(14+21) = 2*22*2*35 = 3080.

Multiple choice

What length of solid cylinder $2$ cm in diameter must be taken to cast into a hollow cylinder of external diameter $12$ cm, $0.25$ cm thick and $15$ cm long ?
  1. $44.0123$ cm
  2. $42.3215$ cm
  3. $44.0625$ cm
  4. $44.6023$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of solid cylinder = Volume of hollow cylinder. pi * r^2 * h = pi * (R^2 - r_inner^2) * H. External diameter 12 means R=6. Thickness 0.25 means r_inner = 5.75. Volume = pi * (36 - 33.0625) * 15 = pi * 2.9375 * 15 = 44.0625 * pi. Solid cylinder radius = 1, so pi * 1^2 * h = 44.0625 * pi. h = 44.0625.

Multiple choice

A rectangular paper $11$ cm by $8$ cm can be exactly wrapped to cover the curved surface of a cylinder of height $8$ cm. The volume of the cylinder is
  1. $66$ $\displaystyle cm^{3}$
  2. $77$ $\displaystyle cm^{3}$
  3. $88$ $\displaystyle cm^{3}$
  4. $121$ $\displaystyle cm^{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The paper wraps the cylinder, so the circumference = 11 cm and height = 8 cm. 2 * pi * r = 11, so r = 11 / (2 * pi). Volume = pi * r^2 * h = pi * (121 / 4 * pi^2) * 8 = 242 / pi = 77.03. 77 is the correct integer.

Multiple choice

A cylinder whose height is equal to $\displaystyle 2\frac{1}{4}$ times its diameter has the same volume as a sphere of radius 4 cm The radius of the base of the cylinder is
  1. $\displaystyle 3\frac{1}{2}$
  2. $3$ cm
  3. $\displaystyle 2\frac{1}{3}$
  4. $\displaystyle 2\frac{2}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 4^3 = 256/3 * pi. Cylinder volume = pi * R^2 * H. H = 2.25 * (2R) = 4.5R. pi * R^2 * 4.5R = 256/3 * pi. 4.5 * R^3 = 256/3. (9/2) * R^3 = 256/3. R^3 = 512/27. R = cube_root(512/27) = 8/3 = 2 and 2/3.

Multiple choice

A solid cylinder has a total surface area of $462$ $\displaystyle cm^{3}$ Its curved surface area is one-third of its total surface area . The volume of the cylinder is :$\displaystyle \left ( \pi =\frac{22}{7} \right )$
  1. $792$ $\displaystyle cm^{3}$
  2. $539$ $\displaystyle cm^{3}$
  3. $495$ $\displaystyle cm^{3}$
  4. $676$ $\displaystyle cm^{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The curved surface area is 462/3 = 154 cm^2. Using the total and curved surface area equations gives radius 7 cm and height 3.5 cm, so the volume is pi x 7^2 x 3.5 = 539 cm^3. The surface-area unit in the question should be cm^2.

Multiple choice

Cylinder A has a radius 2 cm and a height of 4 cm. Cylinder B has a radius 1 cm and a height of 5 cm. Which cylinder has the greater surface area? (use $\displaystyle \pi =3.14$).

  1. Cylinder A is lesser than B

  2. Cylinder A and B

  3. Cylinder B

  4. Cylinder A
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total surface area of a cylinder is given by 2 * pi * r * (r + h). For Cylinder A, the surface area is 2 * pi * 2 * (2 + 4) = 24 * pi, and for Cylinder B, it is 2 * pi * 1 * (1 + 5) = 12 * pi. Since 24 * pi is greater than 12 * pi, Cylinder A has the greater surface area.

Multiple choice

The radius of a right circular cone $A$ is $\dfrac {1}{5}$ of the radius of right circular cone $B$, and the height of right circular cone A is $\dfrac {1}{4}$ of the height of right circular cone B. Calculate the ratio of the volume of right circular cone A to the volume of right circular cone B.
  1. $\dfrac {1}{16}$
  2. $\dfrac {1}{25}$
  3. $\dfrac {1}{64}$
  4. $\dfrac {1}{80}$
  5. $\dfrac {1}{100}$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h. Ratio = (rA^2 * hA) / (rB^2 * hB). Given rA = rB/5 and hA = hB/4. Ratio = ((rB/5)^2 * (hB/4)) / (rB^2 * hB) = (1/25 * 1/4) = 1/100.

Multiple choice

A right cylinder has radius $5$ and height $5$. If $A$ and $B$ are points on the surface, what is the maximum possible (line) distance between them?
  1. $5$
  2. $5\sqrt{12}$
  3. $10$
  4. $12.5$
  5. $5\sqrt{5}$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The maximum distance between two points on a cylinder is the diagonal of the rectangle formed by the height and the circumference (if unrolled) or the diameter. Here, height=5, radius=5 (diameter=10). The diagonal is sqrt(10^2 + 5^2) = sqrt(125) = 5*sqrt(5).