Question

1)Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump.
(Use π = 3.14)

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Answer 1

Answer:

here is ur answer

Clearly the volume of the water in the overhead tank is equal to the volume of the water removed from the sump.

Now Volume of water in the overhead tank =3.14×0.6×0.6×0.95m

3

=3.14×0.36×0.95m

3

Volume of water in the sump when it is full of water =1.57×1.44×0.95m

3

=1.57×4×0.36×0.95m

3

=2×3.14×0.36×0.95m

3

Volume of water left in the sump after filling the tank

(2×3.14×0.36×0.95−3.15×0.36×0.95)m

3

=3.14×0.36×0.95m

3

Area of the base of the sump =1.57×1.44m

3

=1.57×4×0.36m

3

=2×3.14×0.36m

3

Height of the water in the sump =

2×3.14×0.36

3.14×0.36×0.95

m=

2

0.95

=47.5cm

Now

capacityofsump

capacityoftank

=

2×3.14×0.36×0.95

3.14×0.36×0.95

=

2

1

Step-by-step explanation:

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Answer 2

Hey Mate ! Here is your Answerrr !

__________________________

Given :

• dimensions of the sump = 1.57m×1.44m×95 cm
• Dimensions of Overhead tank

1. Hieght =95cm
2. Radius = 60 cm

• π = 3.14

To Find :

If the water in sump is full and us transferred to overhead pump, how much water will be left in sump if overhead tank become full.

Formula To be used :

We will here use the formula of volume of cuboid and volume of cylinder ,

• Volume of cuboid = l×b×h
• Volume of cylinder = πr²h

Process :

We will use the following steps :

• First we will convert all the units in metre as it is SI unit of length .
• Now, we will find the volume of the cuboidal tank .
• Then, we will find the volume of cylindrical tank.
• then, we will subtract the greater with smaller one.

Solution :

We all know that,

1m = 100 cm

Hence, 95 cm = 95/100 = 0.95 m

60 cm = 60/100 = 0.6 m

Hence, Dimensions if cuboid = 1.57m×1.44m×0.95m

Hence, Volume of cuboid = 1.57×1.44×0.95

$\tt{ \implies volume = 2.14776{m}^{2} }$

Hence, volume of sump = 2.14776m²

Dimensions of cylinder = R(0.6m) and H(0.95)

$\tt{volume = \pi {r}^{2} h}$

$\tt{ \implies volume = \pi \times 0.36 \times 0.95}$

$\tt{ \implies volume = \pi \times 0.342}$

$\tt{ \implies volume = 1.07388 {m}^{2} }$

Hence, Volume of Overhead tank = 1.07388m²

Hence, Water left in Sump

= Volume of Sump - volume of Overhead

= 2.14776m²-1.07388m²

= 1.07388 m²

Hence, Water left in Sump = 1.07388m²

Note : Notice one thing that the volume remaining in sump is the same volume as total volume of Overhead tank. this means that,

volume if sump = 2×volume if overhead sump.

__________________________

Additional Information :

Some formulas related to mensuration :

• Area of square = side²
• perimeter of square = 4×side
• volume of cube = side³
• TSA of cube = 6side²

• Perimeter of rectangle = 2(l+b)
• Area of rectangle = l×b
• Volume if cuboid = l×b×h
• TSA of cuboid = 2(lb+lh+bh)

• Area of circle = πr²
• Perimeter of circle = 2πr
• Volume of sphere = 4/3 πr²
• Volume of cylinder = πr²h
• TSA of cylinder = 2πr(2+h)