Question

A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?

Answer 1

$\boxed{\boxed{\mathbf{440 m^2}}}$
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$\underline\text{We know that}$,

Area of Closed Cylinder = Curved Surface Area of Cylinder + 2(Area of Circle)

=> $\mathsf{2 \pi r h + 2(\pi r^2)}$

=> $\mathsf{2 \pi r (r + h)}$

$\textsf{Area of Closed Cylinder =}$ $\mathsf{2 \pi r h(r + h)}$

$\underline\text{Here}$,

$\mathsf{\pi = \frac{22}{7}}$

$\mathsf{Radius = 7m}$

$\mathsf{Height = 3m}$
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Substituting the values in the Formula, we get,

$\mathsf{2 \times \frac{22}{7} \times 7 (7 + 3)}$

$\mathsf{=> 2 \times 22 (10)}$

$\mathsf{=> 44 \times 10}$

=> $\boxed{\mathbf{ 440 cm^2}}$

Answer 2

Total surface area of a solid cylinder=

curved surface area + sum of the areas of two circular ends of the cylinder

= 2πrh+ 2πr²

Total surface area of a solid cylinder=

2πr(h+r)

The lateral surface area of the curved

surface area of a cylinder= 2πrh

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Solution:

Given:

Radius of Cylindrical tank(r)= 7m

Height of cylindrical tank (h)=3m

Total surface area of cylindrical tank=

2πr(h+r)

Total surface area of cylindrical tank=2× (22/7)×7(3+7)

= 44×10= 440 m²

Total surface area of cylindrical tank= 440

m²

Hence, 440 m² sheet is required .

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Hope this will help you....