Question

A cylinder of curved surface area 1,250 m² is formed from a rectangular metallic
sheet. Find the dimensions of the rectangular sheet if its length is double its
breadth.​

Answer 1

Answer:

given : CSA if cylinder 1250 m², L = 2B

to find dimension of sheet formed out if this

CSA of cylinder = area of rectangular sheet out if which cylinder is formed

therefore area of rectangle = 1250 m²

=> 1250 = L × B = 2B × B [ given L = 2B ]

=> 2B² = 1250

=> B² = 1250/2

=> B² = 625

=> B = 25 cm

=> L = 2B = 2 × 25 cm = 50 cm

L = 50 cm and B = 25 cm

Answer 2

$\Large{\underbrace{\sf{\purple{Required\:Answer:}}}}$

Given :

• A cylinder of curved surfαce αreα 1,250m² is formed from α rectαngulαr metαllic sheet. Length of the rectαngulαr metαllic sheet is double of its breαdth.

To Find :

• The dimensions or the length αnd the breαdth of the rectangulαr sheet.

Knowledge Required :

$\large\star{\boxed{\sf{\purple{Area_{(rectangle)} = length\times breadth}}}}$

Solution :

Let the breαdth αnd the length of the rectαngulαr sheet be x αnd 2x.

According to the question,

$\longrightarrow{\sf{ 2x \times x = 1,250m^{2}}}$

$\:\:\:\:\:\longrightarrow{\sf{ 2x^{2} = 1,250m^{2}}}$

$\:\:\:\:\:\:\longrightarrow{\sf{ x^{2} = \dfrac{1,250m^{2}}{2}}}$

$\:\:\:\:\:\:\longrightarrow{\sf{ x^{2} = 625m^{2}}}$

$\:\:\:\:\:\:\longrightarrow{\sf{ x = \sqrt{625m^{2}}}}$

$\:\:\:\:\:\:\:\:\large\implies{\boxed{\sf{\purple{ 25m}}}}$

So, the breαdth is 25m.

Therefore, the length will be $\displaystyle{\sf{ 2x = 2\times 25}}$

$\large\implies{\boxed{\sf{\purple{ 50m}}}}$

Hence, the length αnd the breαdth of the rectαngulαr sheet is 50m αnd 25m.

╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾