A Social welfare association decides to supply drinking water for the flood affected people. The drinking water is filled in a container which is in the shape of a cylinder with a hemispherical end as shown in the figure. The whole length of the tanker is 4.2 metre and the diameter of the base if the cylinder and two hemispheres are each 1.2 metre. If they distribute drinking water to 60 people in a container, each is in the shape of a cylinder of radius 21 cm, find the quantity of water left in the tanker after distribution in litre.(use π = 22/7)

1,499 liter

Step-by-step explanation:

The rest of the question is:

each is in the shape of a cylinder of radius 21 cm and height is 50 cm.

The quantity of water left in the tanker after distribution

= Total quantity - Distributed quantity

Total quantity = Volume of the giving figure

                       = Volume of the cylinder + volume of 2 hemispheres

Volume of the cylinder of 4.2 m length and 1.2 m of a diameter.

L = 4.2 and radius = r = 0.5 * diameter = 0.5 * 1.2 = 0.6

Volume of cylinder = π r² L = (22/7) * 0.6² * 4.2 = 4.752 m³

Volume of 2 hemispheres = 2*0.5 * (4/3) π r³ = (4/3) * (22/7) * 0.6³

                                           =792/875 m³

Total volume = 4.752 + 792/875 = 198/35 ≈ 5.657 m³

Distributed quantity = 60 times the volume of a cylinder of radius 21 cm and height is 50 cm

Distributed quantity = 60 * π r² L = 60 * (22/7) * 21² * 50 = 4,158,000 cm³

Since 1 m³= 1,000,000 cm³

Distributed quantity = 4,158,000 cm³ = 4.158 m³

The quantity of water left in the tanker after distribution =

 = 198/35 - 4.158 ≈ 1.499 m³

Since 1 m³= 1,000 liter

The quantity of water left in the tanker after distribution =

  =  1.499 m³ = 1.499 * 1000 = 1,499 liter

142 liters

Step-by-step explanation:

The following information is missing:

"if they distributing drinking water to 60 people in a container each in shape of cylinder of radius 21 cm and height 50 cm"

If we subtract the two hemispheres, the length of the tank is 4.2 -1.2 = 3 m. The tank is composed by an sphere and a cylinder (with a diameter = 1.2 m). Then, its volume is

Volume of the tank =  π*D²/4*lenght + 4/3*π*D³/8

Volume of the tank =  22/7*1.2²/4*3 + 4/3*22/7*1.2³/8 = 4.3 m³

On the other hand, each small container is a cylinder of radius 0.21 m and height 0.5 m. Each one has a volume of:

Volume of the small container = π*r²*height

Volume of the small container = 22/7*0.21²*0.5 = 0.0693 m³

For 60 containers the total volume is 0.0693*60 = 4.158 m³

Then, the volume left in the tank after the distribution is 4.3 - 4.158 = 0.142 m³ or 142 liters

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}