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 total surface area of a hemisphere is 41.58 cm.2. Find its curved surface area. एक गोलार्द्ध का कुल पृष्ठ क्षेत्रफल 41.58 सेमी.2 है। इसका वक्र पृष्ठ क्षेत्रफल ज्ञात कीजिये ।

  1. 27.72 cm.2/ सेमी.2

  2. 55.44 cm.2/ सेमी.2

  3. 9.24 cm.2/ सेमी.2

  4. 13.86 cm.2/ सेमी.2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total surface area of hemisphere = 3πr². Curved surface area = 2πr². Therefore, curved surface area = (2/3) × total surface area = (2/3) × 41.58 = 27.72 cm².

Multiple choice

If the area of the in-circle of a square is 16π cm.2, then what will be the area of the square? यदि एक वर्ग के अंतःवृत्त का क्षेत्रफल 16π सेमी.2 है, तो वर्ग का क्षेत्रफल क्या होगा ?

  1. 64 cm.2/सेमी.2

  2. 81 cm.2/सेमी.2

  3. 100 cm.2/सेमी.2

  4. 36 cm.2/सेमी.2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of incircle = 16π = πr², so radius r = 4 cm. For a square, the incircle touches all four sides, meaning the diameter equals the side length. Therefore, square side = 2r = 8 cm. Area of square = side² = 8² = 64 cm². The relationship between incircle radius and square side is the key insight.

Multiple choice

A rectangular sheet of metal is 40 cm by 15 cm. Equal squares of side 4 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is-
  1. $896 cm3$
  2. $1288 cm3$
  3. $985 cm3$
  4. $869 cm3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When 4cm squares are cut from each corner and folded up, the new box dimensions are: length = 40-2(4) = 32cm, width = 15-2(4) = 7cm, height = 4cm. Volume = length × width × height = 32 × 7 × 4 = 896 cm³. This is an optimization problem where cutting squares creates an open box.

Multiple choice

What would be the cost of fencing a circular field at the rate of Rs. 40 per meter? Statement I: The circumference of the field is 220 metres. Statement II: The area of the field is 616 square metres.

  1. If only statement I is sufficient.

  2. If only statement II is sufficient.

  3. If either I or II is sufficient.

  4. If neither I nor II is sufficient.

  5. If both statements I and II are necessary.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: Circumference = 220m. Cost = 220 × 40 = Rs. 8800 (sufficient). Statement II: Area = 616 = πr² gives r = 14m. Circumference = 2πr = 88m. Cost = 88 × 40 = Rs. 3520 (sufficient). Since either statement alone is sufficient, answer is C.

Multiple choice

The capacities of two hemispherical bowl are 25.6 litre and 86.5 litre respectively. what is ratio of the internal curved surface area?

  1. 2 : 3

  2. 3 : 5

  3. 4 : 5

  4. 4 : 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For hemispheres, the ratio of curved surface areas is (4πr²/2) : (4πR²/2) = r² : R². Since volume of hemisphere = (2/3)πr³, the radii are proportional to the cube roots of volumes. r ∝ ³√25.6 ≈ 2.96, R ∝ ³√86.5 ≈ 4.42. Therefore, r² : R² = (2.96)² : (4.42)² = 8.76 : 19.54 ≈ 4:9. The key insight is that surface area ratio is the square of the cube root ratio of volumes.

Multiple choice

A person wants to make a cylindrical box which is open from the top. If the height of that box is 10cm and radius is 7 cm find the area of sheet which is required to make it.

  1. 880

  2. 1188

  3. 594

  4. 440

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

An open-top cylindrical box requires the base area (circular) plus the lateral (curved) surface area. Base area = πr² = (22/7)×7×7 = 154 cm². Lateral area = 2πrh = 2×(22/7)×7×10 = 440 cm². Total = 154 + 440 = 594 cm².

Multiple choice

In each of the following questions, a question is followed by three statements numbered I, II and III. Read all the statements and answer accordingly. What will be the increase percent in volume? Statement I: An ice cube is dip into 10 liter water Statement II: If radius of a cylinder increases by 20% and height increases by 10% Statement III: If the height of ice cube is 10 cm.

  1. All I, II and III

  2. II alone and I and III together

  3. I and II together

  4. II and III alone

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

Volume of cylinder = πr²h. New radius = 1.2r, new height = 1.1h. New volume = π(1.2r)²(1.1h) = 1.584πr²h. Increase = 58.4%. Statement II alone gives the formula and percentage increases needed. Statements I and III about ice cube (10cm height in 10L water) are irrelevant to calculating the percent increase in cylinder volume. Option B 'II alone and I and III together' is poorly worded but suggests II is the key.

Multiple choice

What will be the cost of painting the four walls of a room if the rate of painting is Rs 25 per square meter? I. Perimeter of the floor is 44 m. II. Height of the wall of the room is 10 m. III. Ratio of length and breadth of the room is 3:1.

  1. All

  2. I and II

  3. Any one

  4. I and either II or III

  5. Can not be answered even with all the these statements together.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I (perimeter = 44 m) and Statement II (height = 10 m) together are sufficient. The total wall area = perimeter × height = 44 × 10 = 440 sq m. Cost = 440 × 25 = Rs 11,000. Statement III alone is insufficient, and I + III can solve but are not required when both I and II are available.

Multiple choice

The area of the largest circle that can be drawn inside a rectangle with sides 10m by 8m is :

  1. 12 πm2

  2. 14 πm2

  3. 16 πm2

  4. 28 πm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

आयत के अंदर खींचा जा सकने वाला सबसे बड़ा वृत्त आयत की छोटी भुजा के बराबर व्यास वाला होता है। यहां छोटी भुजा 8m है, इसलिए त्रिज्या 4m होगी। वृत्त का क्षेत्रफल = πr² = π × 4² = 16π m²। विकल्प A और B गलत गणना से आते हैं, जबकि D अधिक है।

Multiple choice

Two circles touch each other externally. The sum of their areas is (130\pi) cm2, and the distance between their centers is 14 cm. What will be the radii of the circles?

  1. 11 cm, 3 cm

  2. 9 cm, 4 cm

  3. 8 cm, 5 cm

  4. 9 cm, 5 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For externally touching circles, distance between centers equals sum of radii: r1 + r2 = 14. Areas: pi*r1^2 + pi*r2^2 = 130*pi, so r1^2 + r2^2 = 130. Using (r1+r2)^2 = r1^2 + r2^2 + 2*r1*r2: 14^2 = 130 + 2*r1*r2, giving 196 - 130 = 2*r1*r2, so r1*r2 = 33. The factors of 33 that sum to 14 are 11 and 3. Check: 11+3=14, 11^2+3^2=121+9=130. Option B (9+4=13 not 14), C (8+5=13), D (9+5=14 but 81+25=106).

Multiple choice

There is a circular garden of radius 21 meters. A path of width 3 meters is constructed just outside the garden. What is the area (in meter2) of the path in multiple of π?

  1. 125

  2. 165

  3. 145

  4. 135
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The area of the circular path equals the area of the outer circle minus the area of the inner garden. Inner radius is 21 m, outer radius is 21+3=24 m. Area = π(R² - r²) = π(24² - 21²) = π(576 - 441) = 135π m². Option D correctly shows 135.