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

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. Find the cost of flooring the rectangular hall if perimeter of hall is 320 m and cost of flooring is Rs. 120 per sq.m. (1) The length of rectangular hall is 66.67% more than the breadth of rectangular hall. (2) The area of rectangle hall is 6,000 sq.m.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Both the statements alone are sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Perimeter = 2(L+B) = 320, so L+B = 160. Statement 1: L = 1.6667B = 5/3 B. 5/3 B + B = 160 -> 8/3 B = 160 -> B=60, L=100. Area = 6000. Statement 2: Area = 6000. Both allow finding dimensions and thus cost.

Multiple choice

The following questions are accompanied by two statements (I) and (II). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. (a) Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the questions. (b) Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question. (c) Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question. (d) Either statement (I) or statement (II) by itself is sufficient to answer the question. (e) Statements (I) and (II) taken together are not sufficient to answer the question. What is the volume of the sphere? I. Surface area of hemisphere is equal to the total surface area of the cylinder having radius and height in ratio 3 : 4. II. When we cut sphere into two hemi-sphere then total surface area is equal to the area of a circle whose radius is 21 cm.

  1. A

  2. B

  3. C

  4. D

  5. E
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II provides the radius of the sphere (since surface area of a sphere is 4*pi*r^2 and two hemispheres have total surface area 3*pi*r^2 = area of circle with radius 21, which is pi*21^2). This allows calculation of the volume. Statement I involves a cylinder with unknown dimensions, so it is insufficient.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered) Quantity I : The total surface area of a cone is 1848 square cm. If the slant height is 25 cm more than the radius, then find the volume of the cone Quantity II : A cylinder has height equal to the radius of the sphere having volume 310464 cubic centimetres. The height and the radius of the cylinder are in the ratio 3 : 2 respectively. Find the volume of the cylinder.

  1. Quantity : I > Quantity : II

  2. Quantity : I ≥ Quantity : II

  3. Quantity : I < Quantity : II

  4. Quantity : II ≥ Quantity : I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: TSA of cone = pi*r*(r+l) = 1848. With l = r + 25, pi*r*(2r+25) = 1848. Solving for r gives r=14, l=39, h=sqrt(39^2-14^2)=sqrt(1325) approx 36.4. Volume I approx 7470. Quantity II: Sphere volume = 310464 = 4/3*pi*R^3, so R^3 = 74088, R=42. Cylinder h=42, r=28. Volume II = pi*28^2*42 approx 103683. Thus I < II.

Multiple choice

Directions: A solid consists of a cuboid having length and breadth each equal to 'l' m and the height of the cuboid is 3.14l m. This cuboid is surmounted on a cubical solid of side 'l' m. If it takes around 1 cylindrical jug to fill 0.001 l3 m3. How many jugs would be needed to fill half of the volume of the whole solid. Also, find out how much time it would take to fill the half of the whole volume, if it fills 0.001 l3 m3 in 0.5 seconds.

  1. 1025 and 8 minutes and 25 seconds.

  2. 2050 and 15 minutes and 45 seconds.

  3. 2070 and 17 minutes and 15 seconds.

  4. 1035 and 8 minutes and 37.5 seconds.

  5. 465 and 3 minutes and 47.5 seconds.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cuboid = l * l * 3.14l = 3.14l^3. Volume of cube = l^3. Total volume = 4.14l^3. Half volume = 2.07l^3. Jugs needed = 2.07l^3 / 0.001l^3 = 2070. Time = 2070 * 0.5 seconds = 1035 seconds = 17 minutes and 15 seconds.

Multiple choice

A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long and the other two sides are equal. The perpendicular distance, from the corner of the plot, where the two equal sides meet, to the base, is 200 feet. To counter the adverse effect of climate change, the farmer wants to dig a circular pond. He plans that half of the circular area will be inside the triangular plot and the other half will be outside, which he will purchase at the market rate from his neighbour. The diameter of the circular plot is entirely contained in the base and the circumference of the pond touches the two equal sides of the triangle from inside. If the market rate per square feet of land is Rs. 1,400, how much does the farmer must pay to buy the land from his neighbour for the pond? (Choose the closest option.)

  1. Rs. 3,16,80,000

  2. Rs. 4,25,60,000

  3. Rs. 6,33,60,000

  4. Rs. 7,42,80,000

  5. Rs. 2,98,20,000
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. Find the total surface area of the cone. (1) Radius of the cone is 7 cm. (2) Slant height of the cone is 14 cm.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Surface area of a cone = pi*r*(r + l). We need both radius (r) and slant height (l). Statement 1 gives r, Statement 2 gives l. Both are needed.

Multiple choice

Directions: The question given below consists of a statement followed by Quantity I and Quantity II. Find the relationship between the quantities and choose the answer accordingly. The length of a rectangle is 6 cm more than its width and the area of the same rectangle is 60 cm more than 5 times its perimeter. Quantity I: If the breadth of the rectangular is increased by 5 cm and the length of the rectangle is decreased by 1 cm, what could be the area of the shape formed? Quantity II: If the breadth of the rectangle is increased by 4 cm, what could be the area of the rectangle?

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let width be w, length be w+6. Area = w(w+6) = w^2 + 6w. Perimeter = 2(2w+6) = 4w+12. Given w^2 + 6w = 5(4w+12) + 60 => w^2 + 6w = 20w + 120. w^2 - 14w - 120 = 0 => (w-20)(w+6) = 0. So w=20, l=26. Quantity I: (20+5)(26-1) = 25*25 = 625. Quantity II: 26(20+4) = 26*24 = 624. 625 > 624.

Multiple choice

A school plans to develop a rectangular botanical garden on its campus. To protect the garden, the authorities decide to fence it on all four sides. However, the side facing the main road is to be fenced with a premium decorative iron fence that costs Rs. 300 per foot, while the other three sides will use standard fencing costing Rs. 150 per foot. The total area of the garden is 1,35,000 square feet, and the school wants to minimise the total fencing cost while enclosing this area. What is the minimum total fencing cost (in INR) of all the four sides of the garden?

  1. 3,66,000

  2. 2,27,000

  3. 2,70,000

  4. 3,60,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let length be L and width be W. Area LW = 135000. Cost = 300L + 150L + 150W + 150W = 450L + 300W. To minimize, use AM-GM: 450L + 300W >= 2 * sqrt(450L * 300W) = 2 * sqrt(135000 * 135000) = 2 * 135000 = 270000.

Multiple choice

Following questions contain two statements as statement I and statement II. You have to determine which statement/s is/are necessary to answer the question and give answer as, What is the height of the cone? Statement I: The height of the cone is 17 cm more than that of the radius of the cone. Statement II: The volume of the cone is 1232 cm2 and the total surface area of the cone is 704 cm2 .

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question

  4. The data given in both statements I and II together are not sufficient to answer the question

  5. The data given in both statements I and II together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: Read the information carefully to answer the question that follows. The premises of a school are to be renovated. The renovation is in terms of flooring. Certain areas are to be floored either with marble or wood. All classrooms/halls and pantry are rectangular. The area to be renovated comprises of a big hall measuring 25 m × 25 m, principal's room measuring 13 m × 17 m, a pantry measuring 14 m × 13 m, a recordkeeping cum server room measuring 21 m × 13 m and locker area measuring 29 m × 21 m. The total area of the school is 2000 square metres. The cost of wooden flooring is Rs. 100 per square metre and the cost of marble flooring is Rs. 150 per square metre. The locker area, recordkeeping cum server room and pantry are to be floored with marble. The principal's room and the hall are to be floored with wood. No other area is to be renovated in terms of flooring.

If the remaining area of the school is to be carpeted at a rate of Rs. 110/- per square metre, then how much will be the increment in the total cost of renovation of school premises?

  1. Rs. 8900

  2. Rs. 9900

  3. Rs. 7900

  4. Rs. 8500

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

Renovated areas: Hall (625), Principal (221), Pantry (182), Server (273), Locker (609). Total renovated = 1910. Remaining area = 2000 - 1910 = 90. The question asks for the increment in cost for this remaining area if carpeted at 110/sqm. 90 * 110 = 9900.

Multiple choice

Passage

Directions: The question given below is followed by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question. Mark your answer as per these codes: (a) (A) and (B) together are sufficient. (b) Either (A) or (B) is sufficient. (c) Only (B) is sufficient. (d) Either (B) alone or (A) and (C) together are sufficient. (e) All are necessary to answer the given question.

The cost of flooring a rectangular plot is Rs. 30 per square metre and its area is 1/3rd the area of a circular field. What will be the total cost of flooring the rectangular plot? (A) The length of the rectangular plot is 42 m. (B) The diameter of the circular field is 42 m. (C) The breadth of the rectangular plot is 3 less than 1/3rd of its length.

  1. a

  2. b

  3. c

  4. d

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

To find the cost, we need the area of the rectangular plot. We know Area_rect = 1/3 * Area_circle. Statement (B) gives the diameter of the circle, allowing us to find its area. Statement (A) gives the length of the rectangle. With area and length, we can find the breadth. Statement (C) provides a relationship between length and breadth. Using (B) and (C) is sufficient, or (A) and (B) is sufficient.

Multiple choice

Passage

Directions: Study the following information carefully and answer the given question. There is a solid cylinder of radius R cm and height h cm. The height of cylinder is 21 cm more than the radius of cylinder. The ratio of the total area of the solid cylinder to the curved surface area of cylinder is 3 : 2. This solid cylinder is cut along vertical axis in N equal pieces. Later it was found that the total surface area has increased by 5292 sq.cm.

Find the radius (R) of the cylinder.

  1. 35 cm

  2. 30 cm

  3. 42 cm

  4. 21 cm

  5. 28 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R be radius, h = R + 21. Total surface area (TSA) = 2*pi*R*(R+h) = 2*pi*R*(2R+21). Curved surface area (CSA) = 2*pi*R*h = 2*pi*R*(R+21). Ratio TSA/CSA = (2R+21)/(R+21) = 3/2. Solving gives 4R + 42 = 3R + 63, so R = 21.

Multiple choice

Passage

Read the following information carefully to answer the questions Rohit have some articles which are in the form of different structures. These are cylindrical, conical, and spherical. Other than solid conical structure, all two are of both types i.e., hollow as well as solid. Volume of a conical article is three times of the volume of a solid cylindrical article while radius of a solid spherical article is half than that the radius of a conical article. Outer radius of hollow cylindrical article is same as radius of solid spherical article while average of outer radius and inner radius of hollow cylindrical article is equal to radius of solid cylindrical article. Height of cylindrical, conical and hollow cylindrical article is same i.e. 14cm Number of solid spherical article is 1/5 of total number of article Rohit have. Number of hollow spherical article is 150% more than number of conical article. Ratio between numbers of solid cylindrical article to number of conical article is 3:2. Total number of hollow cylindrical article is 40% of total numbers of article Rohit have and also ‘20’ more than the total number of solid spherical article Rohit have. Volume of a hollow spherical article is 33,957 cm 3 whose inner radius is half of its outer radius. Volume of a hollow spherical article is 5.25 time of volume of conical article.

Find the curved surface area of one hollow cylindrical article?

  1. 661 cm2

  2. 1232 cm2

  3. 826 cm2

  4. 521 cm2

  5. 1016 cm2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved surface area of hollow cylinder = 2πRh, where R is outer radius and h is height. The inner surface is not counted in 'curved surface area'. With given dimensions, this equals 1232 cm².

Multiple choice

Passage

In the given questions, two quantities are given, one as ‘Quantity 1’ and another as ‘Quantity 2’. You have to determine relationship between two quantities and choose the appropriate option:

Quantity I: The diagonal of the square is 24√2 cm. The area of the square is? Quantity II: The perimeter of the square is 96 cm. Then the area of the square is?

  1. Quantity I> Quantity II

  2. Quantity I< Quantity II

  3. Quantity II ≥ Quantity I

  4. Quantity II ≤ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Diagonal = 24√2 cm. For a square, diagonal = a√2, so a = 24 cm. Area = a² = 576 cm². Quantity II: Perimeter = 96 cm, so 4a = 96 and a = 24 cm. Area = a² = 576 cm². Both quantities equal 576 cm², so the relationship is 'Quantity I = Quantity II' (or E: cannot be established when E means equal).

Multiple choice

Passage

In the following questions, two quantities are given as Quantity I and Quantity II. Find the correct relationship among them.

Quantity I: Area of the square is 7200 cm2 which is four times the area of the rectangle whose length and breadth is in the ratio of 9:8. What is the sum of length and breadth of the rectangle? Quantity II: A rectangular water tank is 300 cm×488 cm is dug inside a circular field. The area of the remaining portion is 12000cm2 . Find the radius of the circular field.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Square area = 7200, so rectangle area = 7200/4 = 1800. Length:breadth = 9:8, so dimensions are 45×40. Sum = 85cm. Quantity II: Tank area = 300×488 = 146400. Remaining area = 12000, so circle area = 146400 + 12000 = 158400. Using πr² = 158400, r = √(158400/π) ≈ 224.5cm. Since 85 < 224.5, Quantity II > Quantity I, so answer is C.