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

The area of the circle touching y- axis and the line $x = c$ is ......sq. units with center lying on the x-axis.
  1. $\pi \mathrm{c}^{2}$
  2. $\displaystyle \frac{\pi \mathrm{c}^{2}}{4}$
  3. $\displaystyle \frac{\pi \mathrm{c}}{2}$
  4. $\displaystyle \frac{\pi}{4\mathrm{c}^{2}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A circle touching the y-axis (x=0) and the line x=c has a diameter of c. Thus, the radius is c/2. The center lies on the x-axis, so the center is at (c/2, 0). The area is pi * r^2 = pi * (c/2)^2 = pi * c^2 / 4.

Multiple choice

A copper wire when bent in the form of a square encloses an area of 484 sq cm if the same wire is bent in the form of a circle the area enclosed by it is (Use $\displaystyle \pi =\frac{22}{7} $)
  1. 412 $\displaystyle cm^{2} $
  2. 616 $\displaystyle cm^{2} $
  3. 500 $\displaystyle cm^{2} $

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

A square with area 484 has a side of 22 cm, so the perimeter (wire length) is 88 cm. A circle with circumference 88 cm has a radius r = 88 / (2 * 22/7) = 14 cm. The area of the circle is pi * r^2 = (22/7) * 14 * 14 = 616 sq cm.

Multiple choice

Three rectangles $\displaystyle A_{1},A_{2}: : and: : A_{3}$ have the same area. Their lengths $\displaystyle a_{1},a_{2}: : and: : a_{3}$ respectively are such that $\displaystyle a_{1}< a_{2}< a_{3}$. Cylinders $\displaystyle C_{1},C_{2}: : and: : C_{3}$ formed from $\displaystyle A_{1},A_{2}: : and: : A_{3}$, respectively by joining the parallel sides along the breadth. Then,
  1. $\displaystyle C_{1}$ will enclose maximum volume.
  2. $\displaystyle C_{2}$ will enclose maximum volume.
  3. $\displaystyle C_{3}$ will enclose maximum volume.
  4. Each of $\displaystyle C_{1},C_{2}\: \: and\: \: C_{3}$ will enclose equal volume.
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

A cylinder of circumference $ 8$ cm and length $21$cm rolls without sliding for $\displaystyle 4\frac{1}{2}$ seconds at the rate of $ 9 $ complete rounds per second. Find the area covered by the cylinder in $\displaystyle 4\frac{1}{2}$ seconds.
  1. $6104$ $\displaystyle cm^{2}$ Area covered by the cylinder in 1 round $= $ its curved surface area.
  2. $6804$ $\displaystyle cm^{2}$ Area covered by the cylinder in 1 round $= $ its curved surface area.
  3. $6404$ $\displaystyle cm^{2}$ Area covered by the cylinder in 1 round $= $ its curved surface area.
  4. $6204$  $\displaystyle cm^{2}$ Area covered by the cylinder in 1 round $= $ its curved surface area.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The circumference is 8 cm and length is 21 cm. In one round, the area covered is the curved surface area: 8 * 21 = 168 cm^2. The cylinder rolls for 4.5 seconds at 9 rounds per second, totaling 40.5 rounds. Total area = 40.5 * 168 = 6804 cm^2.

Multiple choice

STATEMENT - 1: The slant height of frustum of a cone is 4 cm. and perimeters of its circular ends are 18 cm. and 6 cm. then the curved surface area is 48 sq. cm. STATEMENT - 2: Curved surface area of frustum $ = \pi (r_1+r_2) $, where $r_1$ and $r_2$ are radii of the frustum and $l$ is a slant height.

  1. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

  2. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

  3. Statement - 1 is True, Statement - 2 is False

  4. Statement - 1 is False, Statement - 2 is True
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A solid is in the form of a right circular cylinder mounted on a solid hemisphere of radius $14$ cm. The radius of the base of the cylindrical part is $14$ cm and the vertical height of the complete solid is $28$ cm. Find : (i) The volume of the solid (ii)The surface area of the solid (iii) Cost of painting the solid at the rate of Rs.$0.80$ per $cm^{2}$
  1. $\displaystyle 14373\frac{1}{3}\, cm^{3}$, $3080\, cm^{2}$, Rs. $2464$
  2. $\displaystyle 1473\frac{1}{2}\, cm^{3}$, $3582\, cm^{2}$, Rs. $2499$
  3. $\displaystyle 14573\frac{1}{5}\, cm^{3}$, $3810\, cm^{2}$, Rs. $2762$
  4. $\displaystyle 14370\frac{1}{7}\, cm^{3}$, $3087\, cm^{2}$, Rs. $2465$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cylinder height is 28 - 14 = 14 cm. Volume = (1/3)*pi*r^2*h_hemisphere + pi*r^2*h_cylinder = (2/3)*pi*14^3 + pi*14^2*14 = 14373.33 cm^3. Surface area = 2*pi*r^2 (hemisphere) + 2*pi*r*h (cylinder) = 2*pi*14^2 + 2*pi*14*14 = 3080 cm^2. Cost = 3080 * 0.80 = 2464.