Question

If a label with “USE & CARE” instructions is to be pasted on the entire outer circumference of the bottom cylindrical portion, then the surface area of the label to be used will be __________.
(Hint : Lateral surface area of cylinder = $2\pi rh$)
 

• A. 770 cm²
• B. 1400 cm²
• C. 3500 cm²
• D. 1540 cm²

Hint:

Always convert mm\textsuperscript{2} to cm\textsuperscript{2} by dividing by 100. Use $\pi \approx 3.14$ unless told otherwise.

Answer 1

The Correct Option is D

To determine the surface area of the label that needs to be pasted along the outer circumference of the bottom cylindrical portion of the fire extinguisher, we need to calculate the lateral surface area of the cylinder.

The formula for the lateral surface area of a cylinder is given by:

A = 2πrh

where r is the radius of the cylindrical base and h is the height of the cylinder.

From the problem description, the diameter of the cylinder's base is 140 mm. Therefore, the radius r is half of the diameter:

r = 140 mm / 2 = 70 mm

We are given the height h of the bottom cylindrical portion as 350 mm.

Now, substituting the known values into the formula:

A = 2 × π × 70 mm × 350 mm

Simplify the expression:

A = 2 × π × 70 × 350

A = 2 × π × 24500

Since π ≈ 3.14, we have:

A ≈ 2 × 3.14 × 24500

A ≈ 154000 mm² = 1540 cm²

Thus, the surface area of the label is 1540 cm².