Question

the lateral surface area of a hollow cylinder is 4224 cm^2.it is cut along its height and formed a rectangular sheet of width 33cm. find perimeter of rectangular sheet? ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\Huge{\textsf{Answer}}$

Given that,

Lateral surface area = 4224 cm^2

Width = 33 cm

To find,

The perimeter = ?

Before finding the perimeter, we've to find the length of the rectangular sheet. When a hollow cylinder is cut it will form a rectangular sheet whose length is equal to the height of the hollow cylinder and width will be equal to imaginary circle (base) of the hollow cylinder.

Now, we'll find the length of the rectangular sheet.

Lateral surface area of the hollow cylinder = Surface area of the rectangular sheet

Area of rectangle = lb

Area of rectangular sheet = lb

4224 cm^2 = l $\times$ 33 cm

$\frac{4224\:cm^2}{33\:cm}$ = l

128 cm = l

Therefore, length = 128 cm

Now, we'll find the perimeter of the rectangular sheet.

We know that,

Perimeter of a rectangle = 2(l+b)

Perimeter of the rectangular sheet = 2(128 cm + 33 cm)

Perimeter of the rectangular sheet = 2(161 cm)

Perimeter of the rectangular sheet = 322 cm

Therefore, perimeter = 322 cm

$\Huge{\boxed{\boxed{\purple{Perimeter = 322\:cm}}}}$