Question

8. 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

$\bf{\huge{Answer}}$

• LSA of a hollow cylinder = 4224 cm² Width of the new rectangle = 33 cm Perimeter = ?

$\displaystyle\underline{\textsf{According to the given Question :}}$

$\displaystyle\sf :\implies LSA \ of \ Cylinder = 2\pi rh$

$\displaystyle\sf :\implies 4224 = 2\times \pi\times r\times 33$

$\displaystyle\sf {\scriptsize\qquad\bf{\because}\:\:\texttt{Breadth = Height}}$

$\displaystyle\sf :\implies 4224 = 66\pi r$

$\displaystyle\sf :\implies \dfrac{4224}{66} = \pi r$

$\displaystyle\sf :\implies 64 = \pi r$

$\displaystyle\sf :\implies\underline{\boxed{\sf r = \dfrac{64}{\pi}}}$

The circumference of the circle will be equal to the length of the rectangular sheet

$\displaystyle\sf :\implies Length = 2\pi r$

$\displaystyle\sf :\implies Length = 2\times \pi \times \dfrac{64}{\pi}$

$\displaystyle\sf :\implies Length = 2\times 64$

$\displaystyle\sf :\implies\underline{\boxed{\sf Length = 128 \ cm}}$

$\displaystyle\underline{\textsf{Perimeter will be :}}$

$\displaystyle\sf = 2(l+b)$

$\displaystyle\sf = 2(128+33)$

$\displaystyle\sf = 2(161)$

$\displaystyle\sf \therefore\:\underline{\textsf{Perimeter will be \textbf{322 cm}}}$

Answer 2

Step-by-step explanation:

perimeter of rectangle =l+l+b+b

given b=33cm

let l= x

perimeter of rectangle= x+x+33+33=0

= 2x+66=0

2x= 66

x= 66/2

x= 33

l= 33

b = 33

perimeter = 2l+2b

= 2(33)+3(33)

=66+99

165

hence, perimeter of traingle is 165

I tried my level best