Question

the lateral surface area of a hollow cylinder is 4224 cm² it is cut along its height and formed a rectangular sheet of width 33 cm find the perimeter
of rectangular sheet​

Answer 1

$\tt\huge{★\:Solution\: :-}$

⠀⠀ ⠀ ⠀⠀

$\tt{Lateral\: surface \:area\: =\:2\:πrh}$

$\tt{=\:4224}$$\tt{cm}^{2}$

$\tt{=}$$\tt{2\:༝}$$\tt\frac{22}{7}༝r༝h$

$\tt{=}$$\tt{4424\:cm}^{2}$

$\tt{rh\:=}$$\tt\frac{4224༝7}{22༝2}$

$\tt{rh\:=\:672 -1}$

⠀⠀ ⠀ ⠀⠀

$\tt{Width\: of \:rectangle\:=\:circumference}$$\tt{of \:cylinder}$

$\tt{33\:=\:2πr}$

$\tt{33\:=\:2\:༝}$$\tt\frac{22}{7}༝r$

$\tt\frac{33༝7}{2༝22}=r$

$\tt{r\:=\:5.25 cm}$

$\tt{substituting\: r\:=\:5.25 \:cm \:- 1}$

$\tt{h\:=\:128 \:cm}$

⠀⠀ ⠀ ⠀⠀

$\tt{Now,\:for \:rectangular\: sheet,}$

$\tt{l\:=\:128 cm \:b\:=33 cm}$

$\tt{perimeter\:=\:2\:(l+b)}$

$\tt{=\:2\:(128+33)}$

$\tt{=\:322 cm}$$\sf\pink{Ans}$

Answer 2

Given :

• The lateral surface area of a hollow cylinder is 4224 cm² it is cut along its height and formed a rectangular sheet of width 33 cm.

To Find :

• Perimeter of rectangular sheet = ?

Solution :

• CSA of cylinder = 4224 cm²
• Breadth of rectangle = 33 cm

Finding the length of the rectangle :

→ Area of rectangle = CSA of cylinder

→ Length × Breadth = 4224

→ Length × 33 = 4224

→ Length = 4224 ÷ 33

→ Length = 128 cm

• Hence,the Length of rectangular sheet is 128 m.

Now, let's calculate the perimeter of rectangular sheet :

→ Perimeter of rectangle = 2(Length + Breadth)

→ Perimeter of rectangle = 2(128 + 33)

→ Perimeter of rectangle = 2(161)

→ Perimeter of rectangle = 322 cm

• Hence,the perimeter of rectangular sheet is 322 cm .