Question

A cylinder of curved surface area 1152 m2

is formed from a rectangular

metallic sheet. Find the dimensions of the rectangular sheet if its length is

double of its breadth.​

Answer 1

Given,

A cylinder of curved surface area 1152m² is formed formed from a rectangular

metallic sheet whose is length is double its breadth.

To Find,

The dimensions of the metallic sheet.

Solution,

Let the breadth be x.

Therefore, length of the sheet = 2x.

The CSA of the cylinder is the same as the area of the rectangular sheet.

CSA of cylinder = 1152m²

So forming an equation,

2x x x =  1152m²

2x² = 1152m²

x² = $\dfrac{1152}{2}$ = 576.

Therefore,

x = $\sqrt{576}$

  = 24 cm

Therefore,

Breadth of the rectangular sheet = x = 24 cm.

Length of the rectangular sheet = 2x = 2 x 24 = 48 cm.

Formulas used:

→ Area of rectangle

→ CSA of cylinder

Surface areas and volumes of Cylinder

→ CSA of cylinder = 2πrh

→ TSA of cylinder = 2πr (r +h)

→ Volume of cylinder = πr²h