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8^{th} Mensuration CBSE Enrichment questions

1. A rectangular tank
can hold 650 litres of milk . if it is 130cm long & 250cm wide , find the
height of the tank.

Solution:

*Volume of*rectangular tank*= 650 litres = 650 × 1000 cm*^{3}^{ }*= 650000 cm*^{3}
We know that

*Volume of a cuboid = l × b × h**650000 = 130 × 250 × h*

*⇒*

*h = (650000)/( 130 × 250 )= 20 cm*

**Therefore, height of the tank = 20 cm**

**2. a hall is of length 16m , breadth 14m & height 5m . Calculate the no: of persons that can be accommodated in the hall , assuming 3.5m**

^{3}**of air is required for each person.**

**Solution:**∴Volume of the hall = length × breadth × height

= 16 × 14 × 5

= 1120 m

^{3}
Volume occupied my 1 man
= 3.5 m

^{3}
3.5 m

^{3 }of air occupied my 1 man
1120 m

^{3 }of air occupied my ( 1/3.5)x 1120= 320 man
Therefore, number of men
that can be accommodated = 32 0 men

2.
A cylinder container with diameter 48cm contains sufficient water to submerge a
rectangular solid of iron with dimensions 33cm x 18cm x 12cm.find the rise in
the level of water when solid is completely submerged.

Solution: Diameter
of cylinder = 48 cm ⇒ Radius of cylinder (r) = 24 cm

Now, when the Cuboid
is completely submerged

Then, Volume of
cylindrical portion formed by original water level and after increase in water
level = volume of cuboid

⇒ πr

^{2}h = 33 cm × 18 cm × 12 cm
22/7 x 24 x 24 x h = 33
cm × 18 cm × 12 cm

h = (33 cm × 18 cm × 12
cm x7)/ 22 x 24 x 24=3.94cm

Hence, the required
increase in water level is 3.94 cm

3.
The difference between the circumference and radius of a circle is 74 cm. Find
the circle diameter.

Solution:
circumference - radius = 74 Þ pd- d/2
=74 Þ 22d/7 - d/2 =74

Þ (44d-7d)/14 =74 Þ 37d
= 74x14 Þ d= (74x14)/37 Þ d
= 28cm

4.
Find the area of the rhombus if the length of each side be 7 cm. and
corresponding altitude is 8 cm

Solution:
area of rhombus = base × height = 7 cm × 8 cm = 56 sq cm

5.
A solid cubical block of fine wood costs rupees 256 at rupees 500/m

^{3}. Find its volume and the length of each side.
Solution:
Let the edge of the cubical box be “a” m.

Rs.
500 is the cost of 1 m

^{3}wood
Rs.
256. is the cost of 1x256/500 m

^{3}wood=0.512m^{3}
So,
Volume of total wood = 0.512m

^{3}
a
x a x a = 0.512m

^{3}
a
x a x a = 0.8 x 0.8 x0.8x

The
length of each side = 0.8m=80cm

6.
What will be the volume of the cylinder in which area of the base is 45 sq.cm
and height is 6 cm?

Solution:
The volume of the cylinder = Area of base x height =45 sq.cm x 6 cm =270cm

^{3}^{}
7.
Area of 4 walls of a room is 108 m

^{2}.If height and length of room is in ratio 2: 5 and height and breadth in ratio 4: 5. Find the area of floor of the room.
Solution: Given: L : H =
5 : 2 Þ H : B = 4 : 5

L : H : B = 20 : 8 : 10

Area of four walls of a
room is =2(l + b) h = 108 Þ (l + b) h = 54

(20 x + 10x) x 8x =
54

240x2 = 54

x

^{2}= 54 / 240
x

^{2}= 0.225
The area of floor of the
room = l x b =l × b = 20x × 10x =200x

^{2}=200x 225= 45m^{2}^{}
8.
If Area of the square inscribed in a semicircle is 2cm

^{2}.Find the area of the Square Inscribed In a full circle.
Solution: Area of square
= 2cm

^{2}
Side of square = square
root of 2

Let r be the radius of
the circle and adjust it like that it forms a right angle triangle

then

r

^{2}= (square root of 2)^{2}+ (square root of 2 / 2)^{2}
r

^{2}= 2 + ( 2 / 4)
r

^{2}= 5 / 2
r = square root of ( 5 /
2)

In a full square the
diagonal of square will be the diameter of the cirlcle.

r = square root of ( 5 /
2) is this so diameter = 2 * square root of (5 / 2)

Diagonal of square = side
* square root of 2

side * square root of 2 =
2 * square root of 5 / square root of 2

side * 2 = 2 * square
root of 5

side = square root of 5

Area of square = r

^{2}
= (square root of 5)

^{2}**= 5 cm**

^{2}

^{}
9.
A cylinder tube open at boyh ends is made of metal. The internal diameter of
the tube is 11.2 cm and its length is 21 cm .The metal everywhere is 0.4 cm
thick . Calculate the volume of the metal correct to 1 place of decimal.

Solution:
Internal diameter = 11.2 cm

Internal
radius= 11.2/2 = 5.6 cm Length of the tube = 21 cm

Volume
of the internal cylinder π r

^{2}h = 22x 5.6x5.6x21/7 =2069.76cm^{2}
External
radius, R = (5.6 + 0.4) cm = 6 cm

Volume
of the external cylinder = πR

^{2}h =22x6x6x21/7=2376cm^{2}
Now,
volume of the metal = Volume of the external diameter – Volume of the internal
diameter = (2376 – 2069.76) cm

^{3 }= 306.24 cm^{3 }= 306.2 cm^{3}^{}
10.
The dimension of an oil tin are 26 m x 26 cm x 45 cm .Find the area of
the tin sheet required for making 20 such tins. If 1 square meter sheet costs
Rs. 10 , find the total cost for making 20 such tins.

Solution
: Area of the tin sheet required = Area of 20 oil tins

=
20 × 2 (lb + bh + hl) = 20x2(26x26+26x45+45x26)=12.06m

^{2}
Cost
of 1 m

^{2}tin sheet = Rs.10
Cost
of 12.064 m

^{2 }tin sheet = Rs.10 2.064 = Rs.120.64
So,
total cost for making 20 such tins = Rs.120.64