Question

A cylindrical water tank of diameter 1.4 meter and height 2.1metre is being fed by a pipe of

diameter 3.5 cm through which water flows at the rate of 2 meter per second. In how much time

will the tank be filled?​

Answer 1

Answer:

Time taken to fill the water tank = 1680 s

Step-by-step explanation:

Given:

• Diameter of the cylindrical tank = 1.4 m
• Height of the tank = 2.1 m
• Diameter of the pipe = 3.5 cm = 0.035 m
• Rate of flow of water = 2m/s

To Find:

• Time taken to fill the water tank

Solution:

First finding the volume of the water tank and the pipe.

Volume of a cylinder is given by,

Volume of a cylinder = π r² h

where r is the radius and h is the height of the cylinder

Hence,

Volume of the tank = 22/7 × (1.4/2)² × 2.1

⇒ 22 × 1.96/4 × 0.3

⇒ 3.234 m³

Now,

Height of the pipe = Speed at which water flows = 2 m

Volume of the pipe = 22/7 × (0.035/2)² × 2

⇒ 22/7 × 0.001225/2

⇒ 1.925 × 10⁻³ m³

Now the time taken to fill the water tank is given by,

Time taken = Volume of water tank/Volume of pipe

Substitute the data,

Time taken = 3.234/1.925 × 10⁻³

⇒ 1.68 × 10³ s

⇒1680 s

Hence the total time taken to fill the water tank is 1680 s.

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.