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 it's length is double it's breadth.
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Answer 1

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.

Solution :-

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

We know that,

$\bigstar\:\:\:\large\underline{\boxed{\green{\mathfrak{Area=Length \times Breadth}}}}$

Now,

$:\implies\:\:\:\sf{1250=2x\times x}$

$:\implies\:\:\:\sf{2x^2 = 1250}$

$:\implies\:\:\:\sf{x^2 = \dfrac{1250}{2}}$

$:\implies\:\:\:\sf{x^2 = 625}$

$:\implies\:\:\:\sf{x = \sqrt{625} }$

$:\implies\:\:\:\sf{x = 25\:m}$

∴ Breadth = 25 m.

Thus,

◖Length = 25 × 2 = 50 cm.

So,

»  Length of the rectangular sheet = 50 cm.

»  Breadth of the rectangular sheet = 25 m.