Question

the curved surface area of a hollow cylinder is 4375 it is cut alongst its height and formed a rectangular sheet of width 35 m find perimemetr of rectangualr sheet

Answer 1

Appropriate Question :-

The curved surface area of a hollow cylinder is 4375 sq. meter. It is cut along its height and formed a rectangular sheet of width 35 m. Find perimeter of rectangular sheet.

$\large\underline{\sf{Solution-}}$

Given that,

The curved surface area of a hollow cylinder is 4375 sq. meter. It is cut along its height and formed a rectangular sheet of width 35 m.

Let assume that length of rectangular sheet be x m.

So, According to given question,

$\rm\implies \:CSA_{(cylinder)} = Area_{(rectangle)}$

$\rm \: 4375 = Length \times width$

$\rm \: 4375 = x \times 35$

$\rm \: x = \dfrac{4375}{35}$

$\rm\implies \:x \: = \: 125$

$\rm\implies \:Length_{(rectangle)} \: = \: 125 \: m$

Now, we have

$\rm \: Length_{(rectangle)} \: = \: 125 \: m$

$\rm \: Width_{(rectangle)} \: = \: 35 \: m$

Now,

$\rm \: Perimeter_{(rectangle)}$

$\rm \: =  \: \: \: 2\bigg(Length_{(rectangle)} + Width_{(rectangle)}\bigg)$

$\rm \: =  \: \: \: \: 2(125 + 35) \:$

$\rm \: =  \: \: \: \: 2 \times 160$

$\rm \: =  \: \: \: \: 320 \: m$

Thus,

$\rm\implies \:Perimeter_{(rectangle)} \: = \: 320 \: m$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

Given :-

The curved surface area of a hollow cylinder is 4375 it is cut along its height and formed a rectangular sheet of width 35 m

To Find :-

Perimeter of the rectangular sheet

Solution :-

We know that

CSA of cylinder = 2πrh

Area of rectangle = l × b

CSA of cylinder = Area of rectangle

4375 = Length × 35

4375/35 = Length

125 = Length

Now,

Perimeter of rectangle = 2(l + b)

Perimeter = 2(125 + 35)

Perimeter = 2(160)

Perimeter = 320 m