Math, asked by itzgeniusguy, 3 months ago

A cylindrical tank has a capacity of 2156 m³. The diameter of its base is 14 m. Then find the depth of the tank.​

Answers

Answered by INSIDI0US
95

Answer:

  • The depth or the height of the tank is 14m.

Step-by-step explanation:

Given :-

  • Volume of the cylinder = 2156 m³.
  • Diameter of its base = 14 m.

To Find :-

  • The depth of the tank.

Basic Terms :-

  • Diameter : The diameter is the length of the line through the center that touches two points on the edge of the circle or any figure.
  • Radius : A line segment extending from the center of a circle or any figure.
  • Volume : Volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object.

Formula Used :-

To find the radius we know that,

Radius = Diameter/2

where,

  • Diameter = 14 m.

To find the depth we know that,

Volume of cylinder = πr²h

where,

  • π = 22/7.
  • r = radius.
  • h = height.

Solution :-

To find the depth of the cylinder it is important to have it's radius. Then firstly we will find out the radius of the cylinder.

Given :

  • Diameter = 14 m.

According to the question by using the formula we get,

↦ Radius = Diameter/2

↦ Radius = 14/2

Radius = 7

Hence, radius of the cylinder is 7 m.

Now we have the radius of the cylinder. So, now we will find out the depth or the height of the cylinder.

Given :

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

According to the question by using the formula we get,

↦ Volume of cylinder = πr²h

↦ 2156 = 22/7 × (7)² × h

↦ 2156 = 22/7 × 7 × 7 × h

↦ 2156 = 22/7 × 49 × h

↦ h = 2156 × 7/22 × 49

↦ h = 15092/1078

h = 14

Hence, depth or the height of the cylinder is 14 m.

Verification

↦ Volume of cylinder = πr²h

↦ 2156 = 22/7 × (7)² × h

↦ 2156 = 22/7 × 7 × 7 × h

Putting h = 14 we get,

↦ 2156 = 22/7 × 49 × 14

↦ 2156 = 22/7 × 686

↦ 2156 = 2156

LHS = RHS

Hence, Verified

Answered by CɛƖɛxtríα
148

★ The depth of the tank is 14 m.

Step-by-step explanation:

Analysis -

‎ ‎ ‎ ‎ ‎In the question, it is given that the capacity of a cylinderical tank whose base diameter is of 14 m is 2156 m³. The question says that we've to find the depth of the cylinderical tank, i.e., its height.

Solution -

First of all, let us recall the formulae for cylinder!

  1. LSA = 2πrh sq.units
  2. TSA = 2πr (h + r) sq.units
  3. Volume = πr²h cu.units

As per the analysis, it is clear that we can find the height of the cylinderical tank by using the formula of volume of cylinder because, the word "capacity" denotes "volume". So, 3rd formula has to be used.

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \underline{ \boxed{ \sf \pmb{V = \pi  {r}^{2}h \: cu.units }}}

Here,

‎ ‎ ‎ ‎ ‎ ‎\twoheadrightarrow V = 2156 m³

‎ ‎ ‎ ‎ ‎ ‎\twoheadrightarrow π = 22/7

‎ ‎ ‎ ‎ ‎ ‎\twoheadrightarrow r = d/2, i.e., 7 m

To find the height of the cylinderical tank, we shall equate the given values in the formula and solve for 'h'.

 \longmapsto{ \sf{2156 =  \dfrac{22}{7}  \times  {(7)}^{2} \times h }} \\  \\  \longmapsto{ \sf{2156 =  \dfrac{22}{ \cancel7}  \times  \cancel7 \times 7 \times h}} \\  \\  \longmapsto{ \sf{2156 = 22 \times 7 \times h}} \\  \\  \longmapsto{ \sf{2156 = 154 \times h}} \\  \\  \longmapsto{ \sf{2156   \div 154 = h}} \\  \\  \longmapsto{ \sf{ \dfrac{ \cancel{2156}}{ \cancel{154}}  = h}} \\  \\  \longmapsto{ \sf{ \dfrac{14}{1}  = h}} \\  \\  \longmapsto \underline{ \boxed{ \sf \pmb{ \red{14 \: m = h}}}}

Hence, the height of the cylinderical tank is 14 m.

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