Question

a cylinder of CSA 1250m² is formed from a rectangle find the diameter of rectangle if length is doubled its breadth

Answer 1

Answer :

Let breadth of rectangular sheet = x

And given length of rectangular sheet is doubled its breadth , So

Length of rectangular sheet = 2 x

Also given Curved surface area of cylinder that is made by rectangular sheet = 1250 cm² ,

Area of rectangular sheet = Curved surface area of cylinder

x ( 2 x ) = 1250

2 x ² = 1250

x ² = 625

x = 25

Therefore ,

Breadth of rectangular sheet = 25 cm

And

Length of rectangular sheet = 2 ( 25 ) = 50 cm

Assume height of cylinder = breadth of rectangular sheet = 25 cm

So,

Circumference of cylinder = Length of cylinder

$$\begin{gathered} \mathrm{\pi }d=50 \\ \Rightarrow \frac{22}{7}\times d=50 \\ \Rightarrow d=50\times \frac{7}{22} \\ \Rightarrow d=\frac{350}{22} \\ \mathbf{\Rightarrow }\mathbf{}\mathit{d}\mathbf{}\mathbf{=}\mathbf{}\mathbf{15}\mathbf{.}\mathbf{90}\mathbf{}\mathbf{cm}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathbf{Ans}\mathbf{}\mathbf{)} \end{gathered}$$