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 slice from a circular pizza of diameter 14 inches is cut in a such a way that each slice of pizza has a central angle of 45°. What is the area of each slice of Pizza(in square inches)?**

A. 16.25

B. 19.25

C. 18.25

D. 17.25

E. None of the Above

###### Answer & Explanation

Answer –**B. 19.25**

**Explanation :**

D = 14

R = D/2 = 14/2 =7

Area of each slice of Pizza =πr² * Θ/360°

= (22/7) * 7 * 7 * (45°/360°)

=19.25**A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?**

A. 160

B. 450

C. 250

D. 325

E. None of the Above

###### Answer & Explanation

Answer –**B. 450**

**Explanation :**

378 = 2 * 3 * 3 * 3 * 7

525 = 3 * 5 * 5 * 7

Highest Common Factor(HCF) = 3 * 7 = 21

Size of largest tile = 0.21 m by 0.21 m

Minimum Number of tiles = (3.78 * 5.25) / (0.21 * 0.21) = 450**Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 784 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?**

A. 154

B. 452

C. 616

D. 512

E. None of the Above

###### Answer & Explanation

Answer –**C. 616**

**Explanation :**

Area = 784 cm²

a = 28 cm

Perimeter of Square = 4 * 28

Circumference of a Circle = 4 * 28 * 22/7

2πr = 4 * 4 * 22

r = 16 * 22 * 7 / 2 * 22 = 56 cm

Radius of Circle B = 56/4 = 14 cm

Area of Circle = πr² = 22/7 * 14 * 14 = 616 cm²**The area of a rectangle is equal to the area of a square whose diagonal is 12√6 metre. The difference between the length and the breadth of the rectangle is 6 metre. What is the perimeter of rectangle ? (in metre).**

A. 160 metre

B. 80 metre

C. 82 metre

D. 84 metre

E. None of the Above

###### Answer & Explanation

Answer –**D. 84 metre**

**Explanation :**

d = a√2

12√6 = a√2

a = 12√3

l * b = a² = (12√3)² = 432

l – b = 6 ; l = b + 6

(b + 6)*(b) = 432

b² + 6b – 432 = 0

b = 18; l = 24

2(l + b) = 2(24 + 18) = 84m**The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units.If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the length and breadth of the rectangle.**

A. 15m, 9m

B. 17m, 9m

C. 14m, 7m

D. 16m, 7m

E. None of the Above

###### Answer & Explanation

Answer –**B. 17m, 9m**

**Explanation :**

Length = x; Breadth =y

xy – (x-5)(y+3) = 9

3x – 5y – 6 = 0 —(i)

(x+3)(y+2) – xy = 67

2x + 3y -61 = 0 —(ii)

solving (i) and (ii)

x = 17m ; y = 9m- Height of a cylindrical jar is decreased by 36%. By what percent must the radius be increased, so that there is no change in its volume?

A. 25%

B. 35%

C. 45%

D. 50%

E. None of the Above

###### Answer & Explanation

Answer –**A. 25%**

**Explanation :**

volume of cylindrical jar = Πr1²h

volume of cylindrical jar = Πr2²(64/100)*h = (16/25)*Πr2²h

r2²/r1² = 25/16

r2 /r1 = 5/4

(r2 – r1)/r1 = (5 – 4)/4 * 100 = 25% **The sum of the radius and height of a cylinder is 19m. The total surface area of the cylinder is 1672 m², what is the volume of the cylinder?(in m³)**

A. 3080

B. 2940

C. 3220

D. 2660

E. 2800

###### Answer & Explanation

Answer –**A. 3080**

**Explanation :**

r + h = 19 m

2πr(r + h) = 1672

r = 1672 * 7/ 2 * 22 * 19 = 14

r = 14 ; h = 5

volume of the cylinder = πr²h = (22/7) * 14 * 14 * 5 = 3080 m³**If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192m². What is the area of original rectangle?**

A. 100m²

B. 150m²

C. 175m²

D. 200m²

E. None of the Above

###### Answer & Explanation

Answer –**D. 200m²**

**Explanation :**

length of rectangle = l m

breadth of rectangle = b m

l * (120/100) * b * (80/100) = 192

1.2l * 0.8b = 192

lb = 192 / 1.2 * 0.8 = 200 m²**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?**

A. 14 cm

B. 28 cm

C. 7 cm

D. 56 cm

E. 24 cm

###### Answer & Explanation

Answer –**B. 28 cm**

**Explanation :**

4x = curved surface area = 1232

x = 308

5x = total surface area = 1540

curved surface area = 2πrh

total surface area = 2πr(r + h)

2πr(r + h) = 1540

2πr² + 2πrh = 1540

2πr² = 1540 – 1232

r = 7; h = 28**The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?**

A. 38.57 cm

B. 23.57 cm

C. 42.46 cm

D. 47.47 cm

E. None of the Above

###### Answer & Explanation

Answer –**A. 38.57 cm**

**Explanation :**

Perimeter of square = 2 x Perimeter of rectangle

= 2 * 2 (8+7) = 60 cm.

Side of square = 60/4 = 15 cm = Diameter of semi-circle

Circumference of semi-circle = πd/2 + d

= (22/7) * 2 * 15 + 15 = 38.57 cm

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