Question

A rectangular sheet of tin foil of dimension 66 cm x 12 cm is rolled along its length to form a cylinder. find the volume of the cylinder so formed​

Answer 1

Answer:

$\bigstar{\bold{Volume\:of\:the\:cylinder=4154.22\:cm^{3}}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

Breadth (b) = 12 cm

Length (l) = 66 cm

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

Volume of the cylinder formed

$\Large{\underline{\underline{\bf{Solution:}}}}$

➣ Here the rectangle is converted in to the cylinder.

➣ Hence the area of the rectangle is the curved surface area of the cylinder

➣ The CSA of the cylinder is given by

    CSA = 2 π r h

➣ Here height of the cylinder is the breadth of the rectangle

➣ Hence

    l × b = 2 π r h

➣ Substitute the datas,

    66 × 12 = 2 × 3.14 × r × 12

    66 = 6.28 r

    r = 66/6.28

    r = 10.5 cm

➣ Hence the radius of the cylinder is 10.5 cm

➣ Now the volume of the cylinder is given by the equation,

➣ Volume of a cylinder = π r² h

➣ Substituting the values,

    Volume of the cylinder = 3.14 × 10.5 × 10.5 × 12

    Volume of the cylinder = 4154.22 cm³

$\boxed{\bold{Volume\:of\:the\:cylinder=4154.22\:cm^{3}}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Volume of a cylinder is given by

  Volume of a cylinder = π r² h

→ CSA of a cylinder = 2 π r h

→ TSA of a cylinder = 2 π r (r + h)