Question

a cylindrical tank has a capacity of 2156 m³ and diameter of its base is 14 m. If π = 22/7, find the depth of the tank.​

Answer 1

Given:-

• Capacity of cylindrical tank is 2156m³.
• Diameter of it's base = 14m
• Radius = D/2 = 14/2 = 7m

Solution :-

Let 'h' be considered as height of cylinder.

Now,

Volume of cylindrical tank = 2156m³

⇒ πr²h = 2156m³

⇒ 22/7 × (7)² × h = 2156m³

⇒ 154 × h = 2156m³

⇒ h = 2156 / 154m

⇒ h = 14m

As we know that, height of cylinder is equal to the depth of the tank. Therefore, depth of cylindrical tank is 14m.

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Formula Used:-

Volume of cylinder = πr²h

Extra Formulas:-

• TSA of cylinder = 2πrh + 2πr²

• CSA of cylinder = 2πrh

• Base area of cylinder = πr²

• Height of cylinder = V/πr²

Answer 2

Answer:

Given :-

• A cylindrical tank has a capacity of 2156 m² and diameter of its base is 14 cm. (π = 22/7)

To Find :-

• What is the depth of the tank.

Formula Used :-

$\sf\boxed{\bold{\large{Volume\: of\: cylinder\: =\: {\pi}{r}^{2}h}}}$

where,

• r = Radius
• h = Height

Solution :-

First we have to find the radius,

We know that,

★ $\sf Radius\: =\: \dfrac{Diameter}{2}$ ★

Given :

• Diameter = 14 m

According to the question by using the formula we get,

⇒ $\sf Radius\: =\: \dfrac{14}{2}$

⇒ $\sf Radius\: =\: \dfrac{\cancel{14}}{\cancel{2}}$

➠ $\sf\bold{Radius\: =\: 7\: m}$

Now, we have to find the height,

Let, the depth or height of a tank be h

Given :

• Volume of cylinder = 2156 m³
• Radius = 7 m
• π = 22/7

According to the question by using the formula we get,

↦ $\sf Volume\: of\: cylinder\: =\: {\pi}{r}^{2}h$

↦ $\sf 2156\: =\: \dfrac{22}{7} \times {(7)}^{2} \times h$

↦ $\sf 2156\: =\: \dfrac{22}{7} \times 7 \times 7 \times h$

↦ $\sf 2156\: =\: \dfrac{22}{7} \times 49 \times h$

↦ $\sf h\: =\: \dfrac{2156 \times 7}{22 \times 49}$

↦ $\sf h\: =\: \dfrac{15092}{1078}$

↦ $\sf h\: =\: \dfrac{\cancel{15092}}{\cancel{1078}}$

➦ $\sf\red{h\: =\: 14\: m}$

$\therefore$ The depth or the height of the tank is 14 m .