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 perimeter of a circle and a rectangle is equal. The measure of the sides of the rectangle is 18 cm. and 26 cm. respectively. What will be the diameter of the circle? एक वृत्त और एक आयत का परिमाप समान है। आयत की भुजाओं की माप क्रमशः 18 सेमी. और 26 सेमी. है। वृत्त का व्यास क्या होगा?

  1. 7 cm.

  2. 12 cm.

  3. 49 cm.

  4. 14 cm.

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Perimeter of rectangle = 2(18 + 26) = 88 cm. Circle circumference = 88 cm, so 2πr = 88, thus r = 14.01 cm. Diameter = 2r = 28.01 cm. None of the options (7, 12, 49, 14 cm) match. Option E is correct.

Multiple choice

The radius of a circle is more than the height of a right angled triangle by 40%. The base of the right angled triangle is 44 cm. If the area of the right - angled triangle is equal to the area of the circle, then what is the approximate area of the circle? एक वृत्त की त्रिज्या एक समकोण त्रिभुज की त्रिज्या से 40% अधिक है | समकोण त्रिभुज का आधार 44 सेमी. है | यदि समकोण त्रिभुज का क्षेत्रफल वृत्त के क्षेत्रफल के बराबर है, तो वृत्त का लगभग क्षेत्रफल क्या है ?

  1. 79 cm.2

  2. 86 cm.2

  3. 102cm.2

  4. 66 cm.2

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let triangle height = h. Then r = 1.4h. Area equality: (1/2) × 44 × h = π(1.4h)². This gives 22h = π × 1.96h², so h = 22/(1.96π) ≈ 3.57cm. Area = π(1.4 × 3.57)² ≈ 79 cm².

Multiple choice

What is the area of a circle whose radius is equal to the side of a square whose perimetre is 84 metres? यदि एक वर्ग का परिमाप 84 मी. है और वर्ग की भुजा एक वृत्त के त्रिज्या के समान है तो वृत्त का क्षेत्रफल क्या होगा?

  1. 1276 m2 1276 मी.2

  2. 1486 m2 1486 मी.2

  3. 1386 m2 1386 मी.2

  4. 1156 m2 1156 मी.2

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

Square perimeter = 84 m, so side = 84/4 = 21 m. This is the circle's radius. Circle area = πr² = (22/7) × 21² = (22/7) × 441 = 22 × 63 = 1386 m². Option C (1386) matches this calculation exactly when using π = 22/7.

Multiple choice

The total area of a circle and a square is 2611 cm2. The diameter of circle is 42 cm. What is the sum of circumference of circle and perimeter of square? एक वृत्त और एक वर्ग का कुल क्षेत्रफल 2611 सेमी2. है। वृत्त का व्यास 42 सेमी. है। वृत्त की परिधि और वर्ग के परिमाप का योग क्या है?

  1. 272 cm. 272 सेमी

  2. 380 cm. 380 सेमी

  3. 280 cm. 280 सेमी

  4. Can not be determined तय नहीं कर सकते

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Circle: diameter = 42 cm, radius = 21 cm. Area = π(21)² = 1386 cm² (using π = 22/7). Circumference = 2π(21) = 132 cm. Total area = 2611 cm², so square area = 2611 - 1386 = 1225 cm². Square side = √1225 = 35 cm. Perimeter = 4 × 35 = 140 cm. Sum = 132 + 140 = 272 cm, making option A correct.

Multiple choice

The area of a rectangle is equal to the volume of a cylinder whose circumference is 66 m. If length and breadth of the rectangle is 42 m. and 66 m. respectively then what is the height of cylinder? एक आयत का क्षेत्रफल ,एक बेलन के आयतन के समान है जिसकी परिधि 66 मीटर है। यदि आयत की लंबाई और चौड़ाई क्रमशः 42 मी और 66 मी है। तो बेलन की ऊंचाई क्या है?

  1. 8 m. 8 मी.

  2. 12m. 12मी.

  3. 13m. 13मी.

  4. 17m. 17मी.

  5. 20m. 20मी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cylinder circumference = 66 = 2πr, so r = 33/π. Rectangle area = 42 × 66 = 2772. This equals cylinder volume = πr²h = π(33/π)²h = 1089h/π. So 2772 = 1089h/π, giving h = 2772π/1089 = 8π. Therefore height = 8 m.

Multiple choice

The sum of circumference of a circle and perimeter of square is 380 cm. The diameter of circle is 70 cm. What is the sum of area of circle and square? एक वर्ग के परिमाप तथा एक वृत्त की परिधि का योग 380 सेमी. है। वृत्त का व्यास 70 सेमी. है। वृत्त और वर्ग के क्षेत्रफल का योग कितना है?

  1. 5450 sq. cm. 5450 वर्ग सेमी.

  2. 5220 sq. cm. 5220 वर्ग सेमी.

  3. 5080 sq. cm. 5080 वर्ग सेमी.

  4. Can't be determined निर्धारित नहीं किया जा सकता है

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Circle diameter = 70 cm, radius = 35 cm. Circumference = 2πr = 70π ≈ 220 cm. Square perimeter = 380 - 220 = 160 cm, so side = 160/4 = 40 cm. Area of circle = πr² = π(35)² = 1225π ≈ 3850 sq. cm. Area of square = 40² = 1600 sq. cm. Total area ≈ 3850 + 1600 = 5450 sq. cm.

Multiple choice

What would be the cost of laying a carpet on a floor which has its length and breadth in the ratio of 23: 12 and its perimeter 210 feet, if the cost per square feet of laying carpet is Rs. 4.50? फर्श पर एक कालीन बिछाने की लागत क्या होगी, जिसकी लंबाई और चौड़ाई 23: 12 के अनुपात में है और इसकी परिधि 210 फीट है, यदि कालीन बिछाने की प्रति वर्ग फुट लागत रु. 4.50 है?

  1. Rs. 12178

  2. Rs. 11178

  3. Rs. 10178

  4. Rs. 14728

  5. Rs. 13178
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let length = 23x, breadth = 12x. Perimeter = 2(23x + 12x) = 70x = 210, so x = 3. Area = 23x × 12x = 276x² = 276 × 9 = 2484 sq ft. Cost = 2484 × 4.50 = 11178.

Multiple choice

What would be the cost of building a fence around a square plot with area equal to 529 sq. ft. if the price per foot of building the fence is Rs. 68? 529 वर्ग फुट के बराबर क्षेत्र के साथ एक वर्ग भूखंड के चारों ओर एक बाड़ के निर्माण की लागत क्या होगी। यदि बाड़ के निर्माण के प्रति फुट की कीमत रु 68 है तो?

  1. 6256

  2. 6250

  3. 6156

  4. 6150

  5. 6242
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of square plot = 529 sq ft. Side length = √529 = 23 ft. Perimeter = 4 × 23 = 92 ft. Cost of fencing = 92 × 68 = Rs. 6256. The calculation is straightforward: find the side from the area, calculate perimeter, multiply by cost per foot.

Multiple choice

The respective ratio of curved surface area and total surface area of a cylinder is 4:5. If the curved surface area of the cylinder is 1232cm2, What is the height? एक वेलन के वक्रपृष्ठ क्षेत्रफल और की कुल पृष्ठ क्षेत्रफल का क्रमिक अनुपात 4:5 है । यदि बेलन का वक्रपृष्ठ क्षेत्रफल 1232 सेमी2 है, तो ऊँचाई क्या है?

  1. 14 cm

  2. 28 cm

  3. 7 cm

  4. 56 cm

  5. 24 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given CSA/TSA = 4/5 and CSA = 1232. For a cylinder, CSA = 2πrh and TSA = 2πr(r+h). Therefore, 2πrh / 2πr(r+h) = 4/5, which simplifies to h/(r+h) = 4/5. Cross-multiplying: 5h = 4r + 4h, so h = 4r. If CSA = 1232 = 2πr(4r) = 8πr², then r = 7 cm and h = 28 cm. Answer B is correct.

Multiple choice

Four circles having equal radii are drawn with centres at the four corners of a square. Each circle touches the other two adjacent circle. If remaining area of the square is 94.5 cm2, what is the radius of the circle? (in cm.) एक वर्ग के चार कोनों पर केंद्रों के साथ समान त्रिज्या वाले चार वृत्त बनाये जाते हैं। प्रत्येक वृत्त अन्य दो आसन्न वृत्तों को स्पर्श करता है। यदि वर्ग का शेष क्षेत्रफल 94.5 सेमी2 है, तो वृत्त की त्रिज्या क्या है? (सेमी में)

  1. 10

  2. 7

  3. 10.5

  4. 3.5

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

The square has side 2r since circles at adjacent corners touch. Square area = 4r². Four quarter-circles at corners form one full circle of area πr². Remaining area = 4r² - πr² = r²(4 - π) = 94.5. Solving: r² = 94.5/(4 - π) ≈ 110.1, so r ≈ 10.5 cm.

Multiple choice

The ratio of the curved surface area to the total surface area of a cylinder is 3 : 5. Find out the volume of the cylinder if the curved surface is 462 cm2. (π = 22/7) एक सिलेंडर के वक्रपृष्ठ क्षेत्रफल तथा सम्पूर्णपृष्ठ क्षेत्रफल का अनुपात 3:5 है। तो बेलन का आयतन ज्ञात कीजिये यदि वक्रपृष्ठ क्षेत्रफल 462 सेमी2 है। (π = 22/7)

  1. 1228

  2. 1723

  3. 1540

  4. 1617

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a cylinder: CSA/TSA = 2πrh/(2πrh + 2πr²) = h/(h+r) = 3/5. So 5h = 3h + 3r, giving h = 1.5r. Given CSA = 2πrh = 462, substituting h = 1.5r: 2πr(1.5r) = 462. Using π = 22/7: 2 × (22/7) × 1.5 × r² = 462. Solving: r² = 49, so r = 7 cm and h = 10.5 cm. Volume = πr²h = (22/7) × 49 × 10.5 = 1617 cm³.

Multiple choice

A solid is in the form of a right circular cylinder with hemispherical ends. The total length of the solid is 35 cm. The diameter of the cylinder is 1/4th of its height. Find the surface area of the solid. एक ठोस लम्ब वृत्तीय बेलन के रूप में है जिसके सिरे गोलार्ध के रूप है । ठोस की कुल लंबाई 35 सेमी है। सिलेंडर का व्यास इसकी ऊंचाई का 1/4 है। ठोस के सतह क्षेत्रफल ज्ञात कीजिये।

  1. 680 sq. cm 680 वर्ग सेमी

  2. 800 sq. cm 800 वर्ग सेमी.

  3. 770 sq. cm 770 वर्ग सेमी.

  4. 720 sq. cm 720 वर्ग सेमी.

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

Let cylinder height=h and radius=r. Given diameter=h/4, so h=8r. Total length=h+2r=10r=35, thus r=3.5cm. Surface area = cylinder CSA + 2 hemisphere surfaces = 2πrh + 4πr² = 16πr² + 4πr² = 20πr². With r=3.5, area=245π ≈ 770 sq.cm.

Multiple choice

Two circles touch externally. The sum of their areas is 130π cm2 and the distance between their centers is 14 cm. The radius of the smaller circle is-

  1. 2 cm

  2. 3 cm

  3. 4 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let radii be r and R. For external tangency: r + R = 14 cm. Sum of areas: πr² + πR² = 130π, so r² + R² = 130. Squaring the first equation: (r+R)² = r² + 2rR + R² = 196. Substituting: 130 + 2rR = 196, so rR = 33. Solving the quadratic x² - 14x + 33 = 0 gives (x-3)(x-11) = 0, so radii are 3 cm and 11 cm. The smaller radius is 3 cm.

Multiple choice

What is the total surface area of a cone where (r) is the radius and (l) is the slant height?
  1. $\(πr(l + r)\)$
  2. $\(2πr(l + r)\)$
  3. $\(πrl\)$
  4. $\(πrl^2\)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total surface area of a cone includes the base (circle with area πr²) and the curved surface (πrl). Combined: πr² + πrl = πr(l + r). Option B incorrectly doubles this value. Option C is only the curved surface area without the base. Option D has an incorrect squared slant height.

Multiple choice

A solid cube with a volume of (13824 cm^3) is cut into eight cubes of the same volume. The ratio of the surface area of the original cube and the total sum of the surface area of three smaller cubes will be:

  1. 2 : 3

  2. 2 : 1

  3. 4 : 3

  4. 8 : 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume = 13824 = 24³, so original cube side = 24. Original surface area = 6 × 24² = 3456. When cut into 8 equal cubes, each small cube has side = 24/2 = 12. Each small cube surface area = 6 × 12² = 864. Three small cubes total = 3 × 864 = 2592. Ratio = 3456 : 2592 = 4 : 3.