Correct option is C
Given:
- A rectangular sheet of 31.4 cm × 10 cm
- The sheet is rolled across its length to form a cylinder
- Both ends are covered with circular sheets
- We are to find the total surface area of the closed cylinder
Formula Used:
Total Surface Area of a closed cylinder =
2πr² (area of top and bottom) + 2πrh (lateral surface area)
Where:
- r = radius of the base
- h = height of the cylinder
Solution:
Since the sheet is rolled along its length (31.4 cm), this becomes the circumference of the base of the cylinder.
So,
Step 1: Find the radius
Circumference = 2 × π × r = 31.4
Using π ≈ 3.14:
2 × 3.14 × r = 31.4
6.28 × r = 31.4
r = 31.4 ÷ 6.28 = 5 cm
Step 2: Height of cylinder = 10 cm (the width of the rectangular sheet)
Step 3: Calculate total surface area
- Area of two circular ends = 2 × π × r² = 2 × 3.14 × 5² = 2 × 3.14 × 25 = 157 cm²
- Lateral surface area = 2 × π × r × h = 2 × 3.14 × 5 × 10 = 314 cm²
Step 4: Add both areas
Total surface area = 157 + 314 = 471 cm²
Final Answer: (C) 471 cm²
