Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from **Mensuration** that are important for all the competitive exams. We have included some questions that are repeatedly asked in exams !!

**A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 18 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many cm will the water level rise?**

A. 10 cm

B. 18 cm

C. 12 cm

D. 16 cm

E. None of these

###### Answer & Explanation

Answer –**B. 18 cm**

**Explanation :**

Volume of the Rectangular Block = 22 * 18 * 7

Radius of the Cistern = 7 cm

Area of the Cylinder = Π * r² * h = 22/7 * 7 * 7 * h

22/7 * 7 * 7 * h = 22 * 18 * 7; h = 18 cm**If the radius of cylinder is doubled, but height is reduced by 50%. What is the percentage change in volume?**

A. 100%

B. 150%

C. 125%

D. 175%

5. None of these

###### Answer & Explanation

Answer –**A. 100%**

**Explanation :**

R1/R2 = R/2R & H1/H2 = H/H/2

Original Volume = πr²h

New Volume = π(2r)²h/2

Change in Volume**The perimeter of a rectangle and a square is 80 cm each. If the difference between their areas is 100 cm. Find the sides of the rectangle.**

A. 30cm, 10cm

B. 40cm, 15cm

C. 25cm, 10cm

D. 20cm, 30cm

E. None of the Above

###### Answer & Explanation

Answer –**A. 30cm, 10cm**

**Explanation :**

2(l + b) = 4a = 80

l + b = 40; a = 20 => a² = 400

a² – lb = 100; 400 – lb =100; lb = 300

(l – b)² = (l + b)² – 4lb

(l – b)² = 1600 – 1200; l – b = 20;**The length of a wall is 5/4 times of its height. If the area of wall will be 500m². What is the sum of the length and height of the wall?**

A. 55m

B. 45m

C. 40m

D. 50m

E. None of these

###### Answer & Explanation

Answer –**B. 45m**

**Explanation :**

l = 5x; h = 4x ; l * h = 500

20x² = 500 ; x = 5

l + h = 25 + 20 = 45m**A circular path runs round a circular garden. If the difference between the circumference of the outer circle and inner circle is 88m. Find the width of Path?**

A. 14 m

B. 15 m

C. 18 m

D. 13 m

E. None of the Above

###### Answer & Explanation

Answer –**A. 14 m**

**Explanation :**

Width of the Road = R – r

2πR – 2πr = 88

R – r = 14 m**The radius of a circle is 4 m. What is the radius of another circle whose area is 16 times of that first?**

A. 16 m

B. 64 m

C. 256 m

D. 400 m

E. None of these

###### Answer & Explanation

Answer –**A. 16 m**

**Explanation :**

Ratio of areas = (ratio of radii)²

16/1 = (ratio of radii)²

ratio of radii = 4/1

The required radius = 16 m**What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 20 cm and 21 cm?**

A. 27m

B. 28m

C. 29m

D. 25m

E. 15m

###### Answer & Explanation

Answer –**C. 29m**

**Explanation :**

πR² = πr1² + πr2²

πR² = π(r1² + r2²)

R² = (400 + 441)

R = 29**Find the area of a white sheet required to prepare a cone with a height of 21cm amd the radius of 20cm.**

A. 3080 cm²

B. 2300 cm²

C. 3460 cm²

D. 3600 cm²

E. None of these

###### Answer & Explanation

Answer –**A. 3080 cm²**

**Explanation :**

r = 20 ; h = 21

l = √(400 + 441) = 29 cm

Total surface area = πrl + πr² = πr(l + r) = 22/7 * 20(49) = 3080 cm²**A hollow cylindrical tube open at both ends is made of plastic 4 cm thick. If the external diameter be 54 cm and the length of the tube be 490 cm, find the volume of plastic.**

A. 320000 cm³

B. 340000 cm³

C. 306300 cm³

D. 308000 cm³

E. None of these

###### Answer & Explanation

Answer –**B. 640640 cm³**

**Explanation :**

Explanation :

External Radius = 27; Internal Radius = 23

Volume of Plastic =πh(R² – r²) = 22/7 * 490(27² – 23²) = 308000 cm³**A solid metallic cylinder of base radius 5 cm and height 7 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones?**

A. 53500

B. 49500

C. 51500

D. 52500

E. None of these

###### Answer & Explanation

Answer –**D. 52500**

**Explanation :**

Explanation :

Number of cones =Volume of Cylinder / Volume of one cone

= π*5*5*7 / (1/3π * 1/10 * 1/10 * 1)

= 52500

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