Question

A closed cylindrical tank of radius 3.5 m and height 2m is made from

a sheet of metal. How much sheet of metal is required ?​

Answer 1

Answer:

Given :-

• A closed cylindrical tank of radius 3.5 m and height 2 m is made from a sheet of metal.

To Find :-

• How much sheet of metal is required.

Formula Used :-

${\red{\boxed{\large{\bold{T.S.A\: of\: cylinder\: =\: 2{\pi}r(r + h)}}}}}$

where,

• r = Radius
• h = Height

Solution :-

Given :

• Radius = 3.5 m
• Height = 2 m

According to the question by using the formula we get,

⇒ $\sf T.S.A =\: 2 \times \dfrac{22}{7} \times 3.5(3.5 + 2)$

⇒ $\sf T.S.A =\: 2 \times \dfrac{22}{7} \times 3.5(5.5)$

⇒ $\sf T.S.A =\: 2 \times \dfrac{22}{7} \times 3.5 \times 5.5$

⇒ $\sf T.S.A =\: 2 \times \dfrac{22}{7} \times 19.25$

⇒ $\sf T.S.A =\: 2 \times 60.5$

➠ $\sf\bold{\purple{T.S.A =\: 121\: {m}^{2}}}$

$\therefore$ 121 m² of sheet of metal is required.

Answer 2

Answer:

Given :

• Cylindrical tank
• Radius = 3.5 m
• Height = 2m

To Find :

• Amount of metal sheet required to make it

Formula :

Total surface area of a cylinder is 2πr(r+h)

Solution :

Putting up the values at correct places :

➸ 2 x 22/7 x 3.5( 2 + 3.5)

➸ 2 x 22 x 0.5(2+3.5)  { 3.5/7 = 0.5}

➸ 44 x 0.5 x 5.5

➸ 121 sq.m

How did we derive the formula ?

We know that a cylinder is made up of 2 circles and 1 rectangle which is curved up .

➸ We have learnt that the area of 1 circle is :

πr²

2 circles make :

πr² + πr²

➸ We have also learnt that the area of a rectangle is (l x b) . Here another logic to be applied is that the length of the rectangle is the circumference of the cylinder being constructed .

So instead of repeating length we can consider the formula of circumference as

2πr

Now when we are aware that the breadth of the rectangle is the height of cylinder formed ; we conclude the area of the rectangle in the cylinder as :

2πr × h

➸ Adding up both the formulas we get :

2πr² + 2πrh

➸ It can be modified by taking the common term as :

2πr(r+h)