Question

7.
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

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 m

So,

» Length of the rectangular sheet = 50 m

» Breadth of the rectangular sheet = 25 m