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

If the longer side of a rectangle is doubled and the other reduced to half, the area of the new rectangle goes up by - यदि किसी आयत की लम्बी भुजा दो गुना कर दी जाये और दूसरी घटा कर आधी कर दी जाये तो नये आयत का क्षेत्रफल कितना बढ़ जाता है?

  1. 0%

  2. 50%

  3. 100%

  4. 150%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original area = L × B. New area = (2L) × (B/2) = L × B. The new area equals the original area, so the increase is 0%. Doubling one dimension and halving the other cancels out.

Multiple choice

If a cylinder of radius 3.5 meter and height 27 meter is melted and constructed into three identical cone of 3 meter height. What will be the radius of each cone ? एक बेलन जिसकी त्रिज्या 3.5 मी. और ऊँचाई 27 मी. है को पिघलाकर तीन बराबर शंकु बनाए जाते हैं। जिनकी ऊँचाई 3 मी. है तो प्रत्येक शंकु की त्रिज्या क्या होगी ?

  1. 10.25 m/मी.

  2. 10.5 m/मी.

  3. 9 m/मी.

  4. 12.5 m/मी.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cylinder = πr²h = π × 3.5² × 27 = π × 12.25 × 27 = 330.75π. This volume is divided equally among 3 cones, so each cone has volume 110.25π. Volume of cone = (1/3)πR²H. For height 3m: (1/3)πR² × 3 = πR² = 110.25π. So R² = 110.25, giving R = 10.5m.

Multiple choice

A right angle triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. What is the volume of the solid so obtained?

  1. 50 p cm2

  2. 100 p cm2

  3. 125 p cm2

  4. 150 p cm2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When a right triangle is revolved about one of its legs, it forms a cone. The leg we revolve about becomes the height (12 cm), and the other leg becomes the radius (5 cm). The volume of a cone is (1/3)πr²h = (1/3) × π × 5² × 12 = 100π cm³. Option B is correct.

Multiple choice

There circle of radius 3.5cm are placed in such away that each circle touches the other two the area of the portion enclosed by the circle is-

  1. 1 cm3

  2. 2 cm3

  3. 3 cm3

  4. 4 cm3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Three circles of radius 3.5cm, each touching the other two, form an equilateral triangle of centers with side 7cm. The enclosed area is triangle minus three sectors. Triangle area = (√3/4)×7² ≈ 21.22cm². Three 60° sectors = half circle = 0.5×π×3.5² ≈ 19.25cm². Enclosed area ≈ 21.22 - 19.25 ≈ 2cm³ (should be cm², not cm³).

Multiple choice

A sphere of radius 2 cm is put into water contained in a cylinder of base radius 4 cm. If the sphere is completely immersed in the water, the water level in the cylinder rise by- 2 सेमी त्रिज्या वाले एक गोले को एक बेलन जिसमें पानी भरा है तथा जिसकी आधार त्रिज्या 4 सेमी है, में डुबोया जाता है। यदि गोला पूरी तरह से पानी में डूब जाये तो बेलन में पानी का स्तर कितना ऊपर उठ जायेगा ?

  1. 1/3 cm/सेमी

  2. 1/2 cm/सेमी

  3. 2/3 cm/सेमी

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

Volume of sphere = (4/3)π(2)³ = 32π/3 cm³. When immersed, this volume displaces water in the cylinder: π(4)²h = 16πh. Equating: 16πh = 32π/3, giving h = 2/3 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- दो वृत्त एक दूसरे को वाह्य रूप से स्पर्श हैं। उनके क्षेत्रफल का योग 130π सेमी2 है। और उसके केन्द्र के बीच की दूरी 14 सेमी है, तो छोटे वृत्त की त्रिज्या ज्ञात कीजिए।

  1. 2 cm/सेमी

  2. 3 cm/सेमी

  3. 4 cm/सेमी

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

For two circles touching externally with radii r and R: sum of areas πr² + πR² = 130π gives r² + R² = 130, and distance between centers r + R = 14. Substituting R = 14 - r: r² + (14-r)² = 130 simplifies to r² - 14r + 33 = 0. Factoring (r-3)(r-11) = 0 gives r = 3 or 11. The smaller radius is 3 cm.

Multiple choice

Let each side of a square is 20cm. Four equal circle each of radius 10cm, are drawn about the four corners of the square so that each touches two of the others. Find the area enclosed between the circumferences of the circles.

  1. 86 cm2

  2. 314 cm2

  3. 78 cm2

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

The four quarter-circles at the corners of the square together form a complete circle with radius 10 cm. The square has side 20 cm, so its area is 400 cm². The area of the full circle is π × 10² = 100π ≈ 314 cm². The area between the circumferences = area of square - area of circle = 400 - 100π ≈ 400 - 314.16 = 85.84 ≈ 86 cm².

Multiple choice

The base of right prism is a quadrilateral ABCD. Given that AB = 9 cm., BC = 14 cm., CD = 13 cm., DA = 12 cm. and ∠ DAB= 90o. If the volume of the prism be 2070 cm3., then the area of the lateral surface is -

  1. 720 cm.2

  2. 810 cm.2

  3. 1260 cm.2

  4. 2070 cm.2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The base is quadrilateral ABCD with AB = 9 cm, BC = 14 cm, CD = 13 cm, DA = 12 cm, and ∠DAB = 90°. Drawing diagonal BD, we get two right triangles ABD and BCD. In ΔABD: AB² + AD² = BD², so BD² = 9² + 12² = 81 + 144 = 225, hence BD = 15 cm. Area of quadrilateral ABCD = Area of ΔABD + Area of ΔBCD. Area of ΔABD = 1/2 × 9 × 12 = 54 cm². For ΔBCD, using Heron's formula or recognizing it as a 5-12-13 triangle (scaled), the area is 1/2 × 5 × 12 = 30 cm² (where 5 and 12 are the legs if we drop an altitude). Actually, let me recalculate: with sides 13, 14, 15, the area can be found using Heron's formula. Semi-perimeter = (13+14+15)/2 = 21. Area = √(21×8×7×6) = √7056 = 84 cm². Total area = 54 + 84 = 138 cm². Volume of prism = Base area × height = 2070, so height = 2070/138 = 15 cm. Perimeter of base = 9 + 14 + 13 + 12 = 48 cm. Lateral surface area = Perimeter × height = 48 × 15 = 720 cm².

Multiple choice

The base of a pyramid is a rectangle 30 m × 20 m and its slant height to the smaller side of the base is 17 metre. Find its volume of pyramid ? एक पिरामिड का आधार 30 मीटर × 20 मीटर का एक आयत है, और आधार की छोटी भुजा की ओर से इसकी तिर्यक ऊंचाई 17 मीटर है। पिरामिड का आयतन ज्ञात आयतन ज्ञात करें?

  1. 1680 m3

  2. 1800 m3

  3. 1600 m3

  4. 2100 m3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Base area = 30 × 20 = 600 m². Using Pythagorean theorem on the triangular face with base 20 m and slant height 17 m: height = √(17² - 10²) = √(289 - 100) = √189 ≈ 13.75 m. Volume = (1/3) × base area × height = (1/3) × 600 × √189 = 200 × 13.75 ≈ 2750 m³. However, checking the given options, the expected answer is 1600 m³, suggesting a calculation in the source used h = √(17² - 10²) = √189 ≈ 13.75, then V = 1/3 × 600 × 8 = 1600, implying vertical height was taken as 8 m possibly from a different slant height interpretation.

Multiple choice

The internal measures of a cuboidal room are 12 m × 8 m × 4 m. Find the total cost of painting all four walls of room, if the cost of painting is Rs. 8.5 per meter square? एक घनाकार कमरे के आंतरिक माप 12 मी. × 8 मी. × 4 मी. हैं । पुताई की लागत 8.5 रूपये प्रति वर्गमीटर है, तो कमरे की सभी चार दीवारों की पुताई की कुल लागत क्या होगी?

  1. Rs. 680

  2. Rs. 1860

  3. Rs. 1580

  4. Rs. 1360
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The area of four walls of a cuboid is given by 2h(l + b), where l=12m, b=8m, h=4m. Area = 2 × 4 × (12 + 8) = 8 × 20 = 160 m². At Rs. 8.5 per m², total cost = 160 × 8.5 = Rs. 1360. Options A, B, and C are incorrect as they don't match the calculated cost.

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?

  1. 5450 sq. cm.

  2. 5220 sq. cm.

  3. 5080 sq. cm.

  4. Can't be determined

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

Circle diameter = 70 cm so radius = 35 cm. Circumference = 2πr = 2 × 22/7 × 35 = 220 cm. Perimeter of square = 380 - 220 = 160 cm, so side = 40 cm. Area of circle = πr² = 22/7 × 35² = 3850 sq.cm. Area of square = 40² = 1600 sq.cm. Total = 3850 + 1600 = 5450 sq.cm.

Multiple choice

Height of a cone is increased by 20% where as its radius is decreased by 25%. find the percentage change in its volume. एक शंकु की ऊचाई 20% बढ़ा दी गयी जबकि इसकी त्रिज्या 25% कम कर दी गयी इसके आयतन में प्रतिशत बदलाव ज्ञात कीजिये।

  1. 32.5% increase/वृद्धि

  2. 32.5% decrease/कमी

  3. 27.5/increase/वृद्धि

  4. 27.5/decrease/कमी
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original volume = (1/3)πr²h. New height = 1.2h, new radius = 0.75r. New volume = (1/3)π(0.75r)²(1.2h) = (1/3)π × 0.5625r² × 1.2h = 0.675 × (1/3)πr²h. This is 67.5% of original volume, meaning a 32.5% decrease. The calculation is straightforward percentage change.

Multiple choice

A sphere of radius 12 cm melted and casted in to cylinder with radius 6 cm and height 'h'. Find the value of 'h'. 12 सेमी. त्रिज्या वाले एक गोले को पिघलाकर 6 सेमी. त्रिज्या तथा h सेमी. ऊँचाई वाले एक बेलन में ढाला गया। h का मान ज्ञात कीजिए।

  1. 32 cm/सेमी.

  2. 16 cm/सेमी.

  3. 64 cm/सेमी.

  4. 18 cm/सेमी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sphere volume = (4/3)πr³ = (4/3)π(12)³ = 2304π. Cylinder volume = πR²h = π(6)²h = 36πh. Equating: 36πh = 2304π gives h = 64 cm. This uses volume conservation principle - melting and recasting preserves volume.

Multiple choice

A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

  1. 5100 cm2

  2. 5200 cm2

  3. 5700 cm2

  4. 5500 cm2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sheet required to make a conical cap is its curved surface area (CSA) = πrl, where l is the slant height. First calculate slant height using Pythagoras: l = √(r² + h²) = √(7² + 24²) = √625 = 25 cm. CSA = π × 7 × 25 = 175π cm² per cap. For 10 caps: 10 × 175π = 1750π ≈ 5500 cm². Option D is correct.