Question

a cylinder of curved surface area 115 to metre square is formed from a rectangular metallic sheet find the dimensions of the rectangular sheet if its length is doubled of its breadth​

Answer 1

Correct Question :

• A cylinder of curved surface area 1152 m square is formed from a rectangular metallic sheet. find the dimensions of the rectangle sheet if its length is double its breadth

Given :

• A cylinder of curved surface area 1152 metre square is formed from a rectangular metallic sheet.

To Find :

• Length of rectangular sheet = ?
• Breadth of rectangular sheet = ?

Solution :

Let Breadth of rectangular sheet be n and Length of rectangular sheet be 2n

★ According to Question :

➻ Area of rectangle = Lateral Surface Area of cylinder

➻ Length × Breadth = Lateral Surface Area of cylinder

➻ 2n × n = 1152

➻ 2n² = 1152

➻ n² = 1152 ÷ 2

➻ n² = 576

➻ n = √576

➻ n = 24 m

Hence,

• Length of rectangular sheet = 2n = 2(24) = 48 m
• Breadth of rectangular sheet = n = 24 m

⠀⠀━━━━━━━━━━━━━━━━━━━━━

⍜ Verification ⍜

→ 2n × n = 1152

→ 2(24) × 24 = 1152

→ 48 × 24 = 1152

→ 1152 = 1152

⎔ LHS = RHS ⎔

⌬ Hence Verified ! ⌬

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Answer 2

$\large{\boxed{\boxed{\sf Corrrect \: Question}}}$

A cylinder of curved surface area 1152m² is formed from a rectangular metallic sheet find the dimensions of the rectangular sheet if its length is doubled of its breadth.

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we have given the curved surface of a cylinder which is formed from a rectangular metallic sheet If it's length is double of its breadth then we have to find the dimension of Rectangular sheet.

$\large{\boxed{\boxed{\sf How \: To \: Do \: It?}}}$

Here, f1st we let the value of Breadth. So, here I m letting the Length 'x' m then According To Question it's Length is double of its breadth then it's Breadth will be halved of its length which is x/2 m. Then using area of Rectangle which is equal to the curved surface area of cylinder. Solving the eq. we will get the value of 'x' which is our length then using the value of 'x' in breadth we will find it's breadth. Hence, we will got our dimensions of rectangular sheet.

Let's Do It ⚡

$\huge{\underline{\boxed{\sf AnSwer}}}$

_____________________________

Given:-

• Curved surface area of Cylinder = 1152m²
• Length of rectangular sheet is doubled the breadth of Rectangular sheet.

Find:-

• Dimension of Rectangular sheet.

Solution:-

Let, Length of Rectangular sheet be ❛x❜ m

Then, Breadth of Rectangular sheet be ❛x/2❜ m

Here,

$\underline{\boxed{\sf Curved \: surface \: area = Area \: of \: Rectangle}}$

and,

$: \implies \: \: \: \underline{\boxed{\sf Area \: of \: Rectangle = l \times b}}$

So,

$\implies\sf Curved \: surface \: area = l \times b$

$\sf where \small{\begin{cases} \sf C.S.A = 1152 {m}^{2} \\ \sf l = x \: m \\ \sf b = \dfrac{x}{2} m \end{cases}}$

✟ Substituting these values:

$\dashrightarrow\sf Curved \: surface \: area = l \times b$

$\dashrightarrow\sf 1152 = x\times \dfrac{x}{2}$

$\dashrightarrow\sf 1152 = \dfrac{ \: {x}^{2} }{2}$

$\dashrightarrow\sf 1152 \times 2= {x}^{2}$

$\dashrightarrow\sf 2304= {x}^{2}$

$\dashrightarrow\sf \sqrt{2304}= x$

$\dashrightarrow\sf 48m= x$

$\underline{\boxed{\sf \therefore Length\:of\: Rectangle\:is\:48m}}$

$\qquad$______________________

Now,

✒ Breadth = x/2 = 48/2 = 24m

$\underline{\boxed{\sf \therefore Breadth\:of\: Rectangle\:is\:24m}}$

$\qquad$______________________

Hence,

❍ Length of Rectangular sheet = 48m

❍ Breadth of Rectangular sheet = 24m