Question

a) a rectangle sheet of metal measuring its length 22 cm and breadth 7 cm is folded along it length to form a cylinder , find its volume and surface area .
b) the same metal sheet now is to be folded along its breadth , fi d the new volume and hence , the difference between in both the volume .
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Answer 1

Answer:

a) Volume of the cylinder is 269.25 cm³

  the surface area of the cylinder is 230.91 cm²

b) New volume of the cylinder is 85.11 cm³

 The difference between both volumes is 184.11 cm³

Step-by-step explanation:

a)   A rectangle sheet of metal measuring its length 22 cm and breadth 7 cm is folded along its length to form a cylinder. Then the length will be the circumference (C) of the base of the cylinder and the breadth will be the height (h) of the cylinder. Then we first solve the equation of circumference to find the radius. That is,

       $C=2\pi r$

Here C = 22 cm,

      $22=2\times 3.14\times r\\\\r=\dfrac{22}{2\times 3.14} =3.5\ cm$

Now apply the value of 'r' in the formula of the volume of the cylinder. Which is,  

       $V=\pi r^{2} h$

r = 3.5 cm and h = 7 cm

⇒    ∴  $V=3.14\times (3.5)^{2}\times 7\\\\V=269.25\ cm^{3}$

The formula to find the surface area of the cylinder is given as,

⇒      $A=2\pi r(r+h)\\\\A=(2\times 3.14\times 3.5)(3.5+7)\\\\\ \ A =230.91 \ cm^2$   

b) The same metal sheet now is to be folded along its breadth.

Now the circumference = 7 cm and the height = 22 cm.

Then, $r=\dfrac{7}{2\times 3.14} =1.11\ cm$

Therefore, the new volume of the cylinder is given by,

⇒        $V=\pi r^{2} h\\\\V=3.14\times (1.11)^{2}\times 22\\\\V=85.11\ cm^{3}$

The difference between both volumes is given as,

⇒        $269.25-85.11=184.11\ cm^3$