Question

A cylinder of curved surface area 1250m²is formed from a rectangular metallic sheet. Find the dimensions of the rectangular sheet if it's length is double it's breadth ?

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

CSA of Cylinder = 1250 m²

Assumption

Length = 2n metre

Breadth = n metre

$\fbox{Rectangular\;sheet = Curved\;surface\;area\;of\;cylinder}$

As se know that -

Area of rectangle = Length × Breadth

Hence,

2n × n = 1250 m²

2n² = 1250m²

$\tt{\rightarrow n^{2}=\dfrac{1250}{2}}$

n² = 625

n = √625

n = 25

Therefore ,

$\fbox{Length}$

= 2 × 25

= 50 m

$\fbox{Breadth}$

= 25 m

${\boxed{\sf\:{Length=50m\;and\;Breadth=25m}}}$

Answer 2

➟ Curved surface area of rectangle = 1250 m²

Let length of rectangle be 2M and breadth be M.

We know that

Area of rectangle = length × breadth

➟ 2M × M = 1250

➟ 2M² = 1250

➟ M² = 625

➟ M = 25

So,

Length = 2M

➟ 2(25)

➟ 50 m

Breadth = M

➟ 25 m

∴ Dimensions are 25 m and 50 m.

______________________________

☆ VERIFICATION:

From above calculations we have M = 25

So,

Length × Breadth = Area of rectangle

=> 50 × 25 = 1250

=> 1250 = 1250