Question

10. A rectangular sheet of area has area 100cm. It is rolled lengthwise to form a cylinder
Find Its CSA​

Answer 1

The CSA of the rectangular sheet rolled into a cylinder is 100 cm².

Step-by-step explanation:

Step 1:

The area of the rectangular sheet is given as = 100 cm²

Let the length and the breadth of the rectangular sheet be “l” cm & “b” cm respectively.

Therefore, we get the eq. as

l * b = 100

⇒ l = $\frac{100}{b}$ …… (i)

Step 2:

It is given to us that the rectangular sheet is rolled lengthwise to form a cylinder, so we can consider that,

[The height of the cylinder i.e., h] = [The breadth of the rectangle] = b

And,

 

[The length of the rectangular sheet]  = [The circumference of the base of the cylinder i.e., a circle]

i.e., l = 2πr ….. [here r = radius of the base of the cylinder]

⇒ $\frac{100}{b} = 2 * \frac{22}{7}$ * r …… [substituting from (i)]

⇒ r = $\frac{100}{b} * \frac{7}{44}$

⇒ r = $\frac{175}{11b}$ …… (ii)

Step 3:

Thus,  

The curved surface area of the cylinder is given by,

= 2πrh

= 2 * $\frac{22}{7} * \frac{175}{11b}$ * b

=2 * 2 * 25  

= 100 cm²

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