Hello Aspirants.

Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are creating question sample from **Mensuration** that are important for IBPS, SBI, RBI, SSC, LIC and other competitive exams. We have included some questions that are repeatedly asked in exams !!

**A room has floor size of 15*6sq cm. What is the height of the room , if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls ?**

1.1.12cm

2.3.24cm

3.4.29cm

4.2.5cm

5.None of these

###### Answer & Explanation

Answer –**3.4.29cm**

**Explanation :**

lb+lb = lh+hb+lh+hb

2lb = 2h(l+b)

h = lb/l+b

h=15*6/15+6 = 4.29 cm

**What is the volume of a right cone whose cross section is isosceles triangle with a base 10cm and slant height 13cm ?**

1.312.4 Sq cm

2.314.2 Sq cm

3.224.2 Sq cm

4.354.2 Sq cm

5.None of these

###### Answer & Explanation

Answer –**2.314.2 Sq cm**

**Explanation :**

Base of the cone(r) =10/2 = 5 cm

Height of the cone (h)= √169-25 =√144 = 12

Volume = 1/3πr^{2}h

= 22*5*5*12/7*3 = 314.2 Sq cm

**Smallest side of a right angled triangle is 6 cm less than the side of a square of perimeter 60 cm. Second largest side of the right angled triangle is 4 cm less than the length of rectangle of area 80 sq. cm and breadth 5 cm. What is the largest side of the right angled triangle?**

1.10cm

2.9cm

3.12cm

4.15cm

5.None of these

###### Answer & Explanation

Answer –**4.15cm**

**Explanation :**

Side of 1^{st}square = 60/4 = 15 cm.

Smallest side of right angled triangle= 15 −6 = 9 cm.

Length of 2^{nd}rectangle = 80/5 = 16 cm.

Second largest side of the 1strectangle = 16−4 = 12 cm.

Largest side = hypotenuse=√9^2+12^2=15cm

**Circumference of a circle-A is 5/4 times perimeter of a square. Area of the square is 961 sq. cm. What is the area of another circle-B whose diameter is half the radius of the circle-A?**

1.167.3 sq cm

2.125.8 sq cm

3.118.9 sq cm

4.181.2 sq cm

5.None of these

###### Answer & Explanation

Answer –**3.118.9 sq cm**

**Explanation :**

The side of the square = a=√961=31 cm.

Perimeter = 4 X 31 = 124 cm

The circumference of the circle = 5/4 x 124 = 22/7 x 2 x r

Radius = 155*7/44 = 24.6 cm

Half the radius of Circle-A = 12.3 cm.

Radius of Circle-B = 14/2 = 6.15 cm

The area = 22/7 x 6.15 x 6.15 = 54 cm^{2}

**A horse is tethered to a peg with a 16 cm long rope at the corner of a 31 cm long and 27cm wide rectangular grass field. What area of the field will the horse graze?**

1.201.1 cm^{2}

2.251.6 cm^{2}

3.111.2 cm^{2}

4.245.3 cm^{2}

5.None of these

###### Answer & Explanation

Answer –**1.201.1 cm**^{2}

**Explanation :**

Area = [22*16*16/7] / 4

= 5632/7*4 = 201.1 cm^{2}

**The biggest possible circle is inscribed in rectangle of length 10 m and breadth 7 m. Then the area of circle is?**

1.35.8 m^{2}

2.36.5 m^{2}

3.30.5 m^{2}

4.38.5 m^{2}

5.None of these

###### Answer & Explanation

Answer –**4.38.5 m**^{2}

**Explanation :**

Radius = Breadth /2 = 7/2 = 3.5

Area = 22*3.5*3.5/7 = 269.5/7 = 38.5 m^{2}

**In a swimming pool measuring 80 cm x 30 cm, 120 men take a dip. If the average displacement of water by a man is 5 cm cube, What will be the rise in water level ?**

1.1/5 cm

2.1/3 cm

3.1/2 cm

4.1/4 cm

5.None of these

###### Answer & Explanation

Answer –**4.1/4 cm**

**Explanation :**

Total volume displaced by 8 men= 120×5 cm cube

However volume=lxbxh=80x30xh

80x30xh=120×5

h=120*5/80*30 = 600/2400 = 0.25.

so the water level rises by 0.25 cm = ¼ cm

**A cylindrical tank of diameter 14 cm****is full of water. If 9 litres of water is drawn off, the water level in the tank will drop by**

1.230.6 cm

2.223.5 cm

3.233.8 cm

4.238.3 cm

5.None of these

###### Answer & Explanation

Answer –**3.233.8 cm**

**Explanation :**

1 litres = 1000 cm

9 litres = 9000 cm

Volume of cylinder = πr^{2}h

22/7*7*7*h = 11000

h = 9000*7*4/22*7*7 = 233.8 cm

**A circular wire of diameter 42cm is folded in the shape of a rectangle whose sides are in the ratio 6:5. Find the ratio of the enclosed rectangle ?**

1.1080cm^{2}

2.1181cm^{2}

3.1250cm^{2}

4.1800cm^{2}

5.None of these

###### Answer & Explanation

Answer –**1.1080cm**^{2}

**Explanation :**

Radius = 42/2 = 21cm

Circumference = 2*22*21/7 = 132cm

L:b = 6x:5x

Perimeter of the rectangle = 2(6x+5x) = 22x

22x = 132

X = 6

Area = 6x * 5x = 30x*x

=30*6*6 = 1080cm^{2}

**A cylindrical tub of radius 10 cm contains water up to a depth of 25cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 5cm. What is the radius of the iron ball(approximate) ?**

1.19

2.15

3.14

4.17

5.None of these

###### Answer & Explanation

Answer –**3.14**

**Explanation :**

Volume of the ball = volume of the raised water

4*22*r^{3}/3*7 = 22*100*5

r^{3 }= 11000*3*7/88 = 2625

r = 13.79 or 14

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