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 the rectangular sheet.

Answer 1

Given :-

• Area of hollow cylinder = $\sf{4224\: cm^2}$
• Width of the rectangular sheet = 33 cm.

To Find :-

• Perimeter of the rectangular sheet.

Solution :-

We know that,

$\pink\bigstar\:\:$ Width of the rectangular sheet = Circumference of the cylinder.

So,

$:\implies\:\sf{33=2\pi r}$

$:\implies\:\sf{33=2\times \dfrac{22}{7} \times r }$

$:\implies\:\sf{r= \dfrac{33 \times7}{2\times22} }$

$:\implies\:\sf{r= \dfrac{3 \times7}{2\times2} }$

$:\implies\:\sf{r= \dfrac{21}{4} \:cm}$

Now,

▪️$\sf{Lateral\: surface \:area \:of \:cylinder =2\pi rh }$

$:\implies\:\sf{4224=2\times\dfrac{22}{7} \times \dfrac{21}{4} \times h}$

$:\implies\:\sf{h= \dfrac{4224 \times 7 \times 4}{2\times22\times21} }$

$:\implies\:\sf{h= \dfrac{1408 \times 2}{11\times3} }$

$:\implies\:\sf{h= 128 \:cm}$

$\therefore\sf{ h = 128 \:cm}$

• l = 128 cm, b = 33 cm

Perimeter of the sheet = 2(l + b)

= 2(128 + 33)

= 2 × 161

= 322 cm

☯ Hence, the required perimeter = 322 cm.

Answer 2

Step-by-step explanation:

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