Question

a cylindrical water tank of diameter 1.4 M and height 2.1 M is being fed by A pipe of diameter 3.5 CM through which water flow at the rate of 2 m per second in how much time the tank will be filled

Answer 1

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Answer 2

Gɪᴠᴇɴ :

Diameter of a cylindrical water tank is 1.4 m.

$\longmapsto\:\:\bf{Diameter\:(d_t)\:=\:1.4\:m}$

Height of the tank is 2.1 m.

$\longmapsto\:\:\bf{Height\:(h_t)\:=\:2.1\:m}$

Aɴᴅ,

Diameter of a cylindrical pipe is 3.5 cm.

$\longmapsto\:\:\bf{Diameter\:(d_p)\:=\:3.5\:cm\:=\:0.035\:m}$

Water flows through the pipe is 2 m/s.

Tᴏ Fɪɴᴅ :

Time taken to fill the water tank.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ Volume of a cylinder is,

$\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{Volume\:=\:\pi\:r^2\:h\:}}}}}}$

Cᴀsᴇ - 1 :

★ Here we calculate the volume of the cylindrical water tank.

Wʜᴇʀᴇ,

Radius (rₜ) = $\bf{\dfrac{d_t}{2}\:=\:\dfrac{1.4}{2}}$ = 0.7 m

Height (hₜ) = 2.1 m

Tʜᴜs,

✯ Volume of the water tank is,

➻ $\bf{Volume\:=\:\pi\times{(0.7)^2}\times{2.1}\:}$

➻ $\bf{Volume\:=\:\pi\times{0.49}\times{2.1}\:}$

➻ $\bf\blue{Volume_{(tank)}\:=\:1.029\pi\:m^3}$

Cᴀsᴇ - 2 :

★ Here we calculate the volume of the cylindrical pipe.

Wʜᴇʀᴇ,

Radius (rₚ) = $\bf{\dfrac{d_p}{2}\:=\:\dfrac{0.035}{2}}$ = 0.0175 m

Height (hₚ) = Rate of flow of water = 2 m

➛ $\bf{Volume\:=\:\pi\times{(0.0175)^2}\times{2}\:}$

➛ $\bf{Volume\:=\:\pi\times{0.00030625}\times{2}\:}$

➛ $\bf{Volume\:=\:0.0006125\pi\:m^3}$

➛ $\bf\purple{Volume_{(pipe)}\:=\:6.125\pi\:\times{10^{-4}}\:m^3}$

Nᴏᴡ,

➣ Let us assume that t seconds is required to fill the water tank.

Tʜᴜs,

↝ Volume of the water flows through the pipe in t seconds is,

$:\longrightarrow\:\:\bf{6.125\pi\:\times{10^{-4}}\times{t}}$

✯ We have, volume of the water flows through the pipe in t seconds is equal to the volume of the water tank.

$\implies\:\bf{6.125\pi\:\times{10^4}\times{t}\:=\:1.029\pi\:}$

$:\implies\:\bf{t\:=\:\dfrac{1.029\pi}{6.125\pi\:\times{10^{-4}}}\:}$

$:\implies\:\bf{t\:=\:\dfrac{1.029}{6.125}\:\times{10^{4}}\:}$

$:\implies\:\bf{t\:=\:0.168\times{10^4}\:}$

$:\implies\:\bf\pink{t\:=\:1680\:seconds\:=\:28\:minutes}$

$\Large\bf{Therefore,}$

The time taken to fill the water tank is 1680 seconds or 28 minutes.