Question

10. A rectangular piece of paper is 22 cm in length and 10 cm in width. It is rolled
into a cylinder along its length. Find the surface area of this cylinder.
​

Answer 1

Step-by-step explanation:

Suppose, r denotes the Base radius and h be the height, there h =10 cm

Circumference of Base = length of rectangular sheet

2nr=22

So, 2×22/7×r=22

Therefore, r=7/2

Hence, volume of cyclinder =nr^2h

= 22/7×7/2×7/2×10

= 385cm^3 (cube).

Answer 2

Answer:

TSA of the cylinder is 297 cm² and the CSA of the cylinder is 220 cm².

Step-by-step explanation:

Given :-

• A rectangular piece of paper is 22 cm in length and 10 cm in width. It's rolled into a cylinder along its length.

To find :-

• TSA and CSA of the cylinder.

Solution :-

• Length of the rectangular paper = 22 cm
• Width of the rectangular paper = 10 cm

It's rolled into a cylinder along with its length.

Length of rectangular paper = Circumference of the base of cylinder

Then,

Circumference of base = 22 cm

We know that,

Circumference of circle = 2πr

According to the question ,

2πr = 22

→ 2× (22/7) × r = 22

→ r = 22× (1/2) × (7/22)

→ r = 7/2

★ Radius of the cylinder is 7/2 cm.

Width of the rectangular paper = Height of the cylinder

Then,

Height of the cylinder = 10 cm

Now find TSA and CSA of the cylinder.

Total surface area of the cylinder,

= 2πr(h+r)

= [2 × (22/7) × (7/2) × (10+7/2) ] cm²

= [2 × (22/7) × (7/2) × (27/2) ] cm²

= 11× 27 cm²

= 297 cm²

Therefore, the TSA of the cylinder is 297 cm².

Curved surface area of the cylinder,

= 2πrh

= [2 × (22/7) × (7/2) × 10] cm²

= 220 cm²

Therefore, the CSA of the cylinder is 220 cm².