Question

The lateral surface area of a hollow cylinder is 1,188 cm. It is cut along its height to obtain a rectangle. Find the perimeter of the rectangle if the height of the cylinder is 44 cm.
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Answer 1

Answer:

142 cm

Step-by-step explanation:

Lateral surface area of a hollow cylinder = 1188 cm²

Height of the hollow cylinder = 44 cm

Since the hollow cylinder is cut along its height the height becomes the breadth of the rectangle

Let the length and breadth of the rectangle be ' l ' and ' b ' cm respectively

Length of the rectangle ( l ) = Height of the hollow cylinder = 44 cm

We know that

Lateral surface area of hollow cylinder = Area of the rectangle

⇒ 1188 = l × b

⇒ 1188 = 44 × b

⇒ 1188/44 = b

⇒ 27 = b

Perimeter of the rectangle = 2( l + b ) = 2( 44 + 27 ) = 2( 71 ) = 142 cm

Therefore the perimeter of the rectangle is 142 cm.

Answer 2

Given

LSA of a hollow cylinder = 1188 cm²

Height of the cylinder = 44 cm

Now, the cylinder is cut along its height

=> The height becomes the length of the rectangle.

Let the length of the rectangle be x.

Lateral surface area of hollow cylinder = Area of the rectangle

$\implies 1188 =44x$

$\implies x= \dfrac{1188}{44}$

$\implies x = 27 \ cm$

SOMETHING YOU NEED TO KNOW

Area of the rectangle = Length * Breadth

Perimeter of the rectangle = 2(Length + Breadth)

Perimeter

$= 2(27+44)\\= 2(71)\\=142 cm$

$\boxed{\boxed{\bold{Therefore, \ the \ perimeter \ of \ the \ rectangle \ is \ 142 \ cm}}}}}$