Question

The lateral surface area of hollow cylinder is 1188cm2. It is cut along its height to obtain a rectangle find the perimeter of rectangle if the height of the cylinder is 44 centimetre

Answer 1

Answer

• Perimeter of the rectangle is 142 cm

Explanation

Given

• The lateral surface area of hollow cylinder is 118 cm²
• It was cut along its height to obtain a rectangle
• Height of the cylinder = 44 cm

To Find

• Perimeter of Rectangle?

Solution

• So we know that when we cut the cylinder to a rectangle the height will be the breadth of the rectangle and the circumference of the top will be equal to the length of the rectangle
• We shall first find its radius of the cylinder and then the circumference which will finally get our sides . With the sides we can find the perimeter

LSA of the cylinder

➝ LSA = 2πrh

➝ 1188 = 2πr × 44

➝ 1188 = 88πr

➝ 1188/88 = πr

➝ 13.5 = πr

➝ Radius = 13.5/π

• Now the circumference will be equal to the length of the rectangle

Circumference

➝ Circumference = 2πr

➝ Length = 2×π×13.5/π

➝ Length = 2×13.5

➝ Length = 27 cm

Perimeter of the rectangle

➝ Perimeter = 2(l+b)

• Length = 27 cm
• Breadth = 44 cm

➝ Perimeter = 2(27+44)

➝ Perimeter = 2(71)

➝ Perimeter = 142 cm

Answer 2

★ ANSWER :

Perimeter of rectangle = 142cm

Step-by-step explanation:

★ QUESTION :

The lateral surface area of hollow cylinder is 1188cm². It is cut along its height to obtain a rectangle find the perimeter of rectangle if the height of the cylinder is 44cm.

★ GIVEN :

• LSA of cylinder = 1182cm²
• Height of cylinder = Breadth of rectangle
• Height of cylinder = 44cm
• Breadth of rectangle = 44cm

★ CONCEPT USED :

• LSA of cylinder = 2πrh
• Circumference of circle = 2πr
• Perimeter of rectangle = 2(l + b)

★ TO FIND :

• Perimeter of rectangle = ?

★ SOLUTION :

• LSA of cylinder

→ LSA = 2πrh

→ 1182cm² = 2πrh

→ 1182cm² = 2πr × h

→ 1182cm² = 2πr × 44cm

→ 1182cm² = 88cm × πr

→ 1182cm²/88cm = πr

→ πr = 1182cm²/88cm

• Circumference of circle

→ Circumference = 2πr

→ 2πr = 2 × πr

→ 2πr = 2 × 1182cm²/88cm²

→ 2πr = 2 × 1182cm²/88

→ 2πr ≈ 27cm

• Circumference of circle = Length of rectangle

Length of rectangle ≈ 27cm

Breadth of rectangle = 44cm

Perimeter of rectangle = 2(l + b)

Perimeter of rectangle = 2 (27cm + 44cm)

Perimeter of rectangle = 2 × 71cm

Perimeter of rectangle = 142cm

★ ANSWER :

Perimeter of rectangle = 142cm

HOPE IT HELPS YOU !

THANKS !